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          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:label="us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPeriodIncreaseDecreaseAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LocalPhoneNumber" xlink:label="dei_LocalPhoneNumber"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionDomain" xlink:label="us-gaap_RelatedPartyTransactionDomain"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract"/>
          <link:loc xlink:type="locator" xlink:href="btsg-20260331.xsd#btsg_ServicingPeriod" xlink:label="btsg_ServicingPeriod"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAcquiredFromAcquisition" xlink:label="us-gaap_CashAcquiredFromAcquisition"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountingPoliciesAbstract" xlink:label="us-gaap_AccountingPoliciesAbstract"/>
          <link:loc xlink:type="locator" xlink:href="btsg-20260331.xsd#btsg_AmedisysAndLHCBranchesAcquisitionMember" xlink:label="btsg_AmedisysAndLHCBranchesAcquisitionMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisaggregationOfRevenueLineItems" xlink:label="us-gaap_DisaggregationOfRevenueLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax"/>
          <link:loc xlink:type="locator" xlink:href="btsg-20260331.xsd#btsg_BasicEarningsLossPerShareAbstract" xlink:label="btsg_BasicEarningsLossPerShareAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfStockByClassTable" xlink:label="us-gaap_ScheduleOfStockByClassTable"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:label="us-gaap_GoodwillImpairedAccumulatedImpairmentLoss"/>
          <link:loc xlink:type="locator" xlink:href="btsg-20260331.xsd#btsg_LcSublimitMember" xlink:label="btsg_LcSublimitMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityEmergingGrowthCompany" xlink:label="dei_EntityEmergingGrowthCompany"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingIncomeLoss" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingIncomeLoss"/>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments for Repurchase of Redeemable Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchase of redeemable noncontrolling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Purchase of redeemable noncontrolling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Purchase of remaining noncontrolling interest paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienCreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">First lien credit agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienCreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">First Lien Credit Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienCreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">First Lien Credit Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), before Reclassification, after Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net change in fair value, net of tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segments [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations, Net of Tax, Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net income from continuing operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income from continuing operations, net of income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskByTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccrualForInterestRateSwapsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrual For Interest Rate Swaps Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccrualForInterestRateSwapsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accrual for interest rate swaps current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccrualForInterestRateSwapsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest rate swaps</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityIncorporationStateCountryCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Incorporation, State or Country Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityIncorporationStateCountryCode_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Incorporation, State or Country Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred Stock, shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BalanceSheetLocationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Financial Position Location, Balance [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationInventoryCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Inventory, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationInventoryCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Inventories</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Flow, Noncash Investing and Financing Activities Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Supplemental schedule of non-cash investing and financing activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalExpenditureDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Capital Expenditure, Discontinued Operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalExpenditureDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchases of property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Excluding Current Maturities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total long-term liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term debt, net of current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Total long-term debt, net of current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDebtInstrumentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Long-Term Debt Instruments [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDebtInstrumentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Total Outstanding Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Plan Name [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionPurchasePriceAllocationGoodwillExpectedTaxDeductibleAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated goodwill deductible for tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionPurchasePriceAllocationGoodwillExpectedTaxDeductibleAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Goodwill, Expected Tax Deductible, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityOtherShares_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stockholders' Equity, Other Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityOtherShares_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCurrentReportingStatus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Current Reporting Status</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCurrentReportingStatus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Current Reporting Status</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienIncrementalTermLoanTrancheB4PayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">First lien incremental term loan tranche b-5 - payable to lenders at SOFR plus applicable margin.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienIncrementalTermLoanTrancheB4PayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">First Lien Incremental Term Loan Tranche B-4 - Payable To Lenders At Sofr Plus Applicable Margin [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienIncrementalTermLoanTrancheB4PayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">First Lien Incremental Term Loan Tranche B-4 - Payable to Lenders at SOFR plus Applicable Margin</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Accounts, Notes and Loans Receivable, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts receivable, net of allowance for credit losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 2 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Level 2</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments and Contingencies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PharmacySolutionsAndProviderServicesSegmentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pharmacy Solutions and Provider Services Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PharmacySolutionsAndProviderServicesSegmentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Pharmacy solutions and provider services segments.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PharmacySolutionsAndProviderServicesSegmentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Pharmacy Solutions and Provider Services Segments [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasicAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Basic [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasicAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Basic income per share attributable to common shareholders:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_HavenHospiceIncMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Haven Hospice, Inc.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_HavenHospiceIncMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Haven Hospice Inc.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_HavenHospiceIncMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Haven Hospice Inc [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ProductOrServiceAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Product and Service [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Period Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Fiscal Period Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Interest Rate, Stated Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Principal at issuance (as a percent)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountingStandardsUpdate202309Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounting Standards Update 2023-09 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountingStandardsUpdate202309Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ASU 2023-09</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue from Contract with Customer [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityShellCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Shell Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityShellCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Shell Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TaxEffectOfNetShareSettlementOfEquityAwards_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tax effect of net share settlement of equity awards, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TaxEffectOfNetShareSettlementOfEquityAwards_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tax Effect of Net Share Settlement of Equity Awards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TaxEffectOfNetShareSettlementOfEquityAwards_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tax effect of net share settlement of equity awards.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TaxEffectOfNetShareSettlementOfEquityAwards_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Tax effect of net share settlement of equity awards, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotesReceivableNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Notes receivable noncurrent.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotesReceivableNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Notes Receivable Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotesReceivableNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Notes receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Accrued Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DerecognitionOfRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derecognition of redeemable noncontrolling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DerecognitionOfRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derecognition Of Redeemable Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DerecognitionOfRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Derecognition of redeemable noncontrolling interest.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Noncontrolling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Noncontrolling Interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business combination recognized identifiable assets acquired and liabilities assumed noncontrolling interests.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValuePurchaseOfAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, Purchase of Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValuePurchaseOfAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from stock purchase contract issued under tangible equity units, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TrancheB4TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tranche B-4 Term Loan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TrancheB4TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tranche B-4 Term Loan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TrancheB4TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tranche B-4 Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ServiceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Service [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ServiceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash and Cash Equivalents, at Carrying Value, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrealizedGainLossOnInterestRateCashFlowHedgesPretaxAccumulatedOtherComprehensiveIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrealized Gain (Loss) on Interest Rate Cash Flow Hedges, Pretax, Accumulated Other Comprehensive Income (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrealizedGainLossOnInterestRateCashFlowHedgesPretaxAccumulatedOtherComprehensiveIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pre-tax gains</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NotesPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Notes Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NotesPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Notes Payable, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NotesPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Short-term portion of the amortizing notes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock, shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CloudComputing_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cloud computing.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CloudComputing_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cloud Computing</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CloudComputing_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cloud computing</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_KohlbergKravisRobertsCoLPAndWalgreensBootsAllianceIncMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Kohlberg Kravis Roberts &amp; Co. L.P. and Walgreens Boots Alliance, Inc.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_KohlbergKravisRobertsCoLPAndWalgreensBootsAllianceIncMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Kohlberg Kravis Roberts &amp; Co. L.P. and Walgreens Boots Alliance, Inc [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_KohlbergKravisRobertsCoLPAndWalgreensBootsAllianceIncMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">KKR and WBA</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AdjustmentOfRedeemableNoncontrollingInterestToRedemptionAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Adjustment of redeemable noncontrolling interest to redemption amount.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AdjustmentOfRedeemableNoncontrollingInterestToRedemptionAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment Of Redeemable Noncontrolling Interest To Redemption Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AdjustmentOfRedeemableNoncontrollingInterestToRedemptionAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Adjustment of redeemable noncontrolling interests to redemption amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeApproachValuationTechniqueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Approach</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeApproachValuationTechniqueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Valuation, Income Approach [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtRefinancingPaymentOfStructuringFee_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt refinancing, payment of structuring fee.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtRefinancingPaymentOfStructuringFee_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Refinancing, Payment of Structuring Fee</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtRefinancingPaymentOfStructuringFee_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Structuring fee paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Businesses, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash payment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionAcquireeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFilerCategory_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Filer Category</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFilerCategory_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Filer Category</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityNetIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, Net Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityNetIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss attributable to redeemable noncontrolling interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities and Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities, redeemable noncontrolling interests, and equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Long-Term Debt, Current Maturities, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Current Maturities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current portion of long-term debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Less: current portion of long-term debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteStockSplit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stockholders' Equity Note, Stock Split</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteStockSplit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock split description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationCostsOfGoodsSold_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Costs of Goods Sold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationCostsOfGoodsSold_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cost of services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TradeNamesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Trade Names [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TradeNamesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trade Names</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Component, Gross proceeds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Exercise Price Range [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Other Liabilities, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Goodwill, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Goodwill, Beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Goodwill, Ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNoncashIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Noncash Income (Expense), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNoncashIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Noncash Income (Expense)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNoncashIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNoncashIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Effective tax rate recognized in the statements of operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeStockOptionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Stock Options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IssuanceOfDebtAndCommonStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">TEU price per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IssuanceOfDebtAndCommonStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Issuance of Debt and Common Stock Price per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IssuanceOfDebtAndCommonStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Issuance of Debt and Common Stock Price per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IssuanceOfDebtAndCommonStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total, Fair value per unit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IssuanceOfDebtAndCommonStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Total, Fair value per unit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FinancingLeaseObligations_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Financing lease obligations.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FinancingLeaseObligations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing lease obligations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FinancingLeaseObligations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Financing lease obligations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Income (Loss) Available to Common Stockholders, Basic [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Numerator:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ExpensesNotAllocatedAtSegmentLevelAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Expenses not allocated at segment level:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ExpensesNotAllocatedAtSegmentLevelAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Expenses not Allocated at Segment Level [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ExpensesNotAllocatedAtSegmentLevelAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Expenses not allocated at segment level.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired to Liability Assumed, Excess (Less) [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateCashFlowHedgeGainLossReclassifiedToEarningsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Cash Flow Hedge Gain (Loss) Reclassified to Earnings, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateCashFlowHedgeGainLossReclassifiedToEarningsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest received</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareAMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Medicare A.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareAMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Medicare A [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareAMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Medicare A</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareAMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Medicare Part A</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRedeemableNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Redeemable Noncontrolling Interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRedeemableNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business combination recognized identifiable assets acquired and liabilities assumed redeemable noncontrolling interests.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRedeemableNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable noncontrolling interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid in Capital, Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional paid-in capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LessThanThirteenPointZeroZeroMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Less than thirteen point zero zero.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LessThanThirteenPointZeroZeroMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Less Than Thirteen Point Zero Zero [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LessThanThirteenPointZeroZeroMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less than $13.00</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt Issuance Costs, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Issuance Costs, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less: debt issuance costs, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncontrollingInterestAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncontrolling Interest [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareBMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Medicare B.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareBMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Medicare B [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareBMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Medicare B</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareBMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Medicare Part B</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestChangeInRedemptionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncontrolling Interest, Change in Redemption Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestChangeInRedemptionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Change in redemption amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DilutedEarningsLossPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Diluted Earnings Loss Per Share [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DilutedEarningsLossPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Diluted earnings loss per share.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DilutedEarningsLossPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Diluted income per share attributable to common shareholders:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Significant Accounting Policies [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Significant Accounting Policies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TrancheB1TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tranche B-1 Term Loan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TrancheB1TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tranche B-1 Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TrancheB1TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tranche B-1 Term Loan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotionalAmountToHedgeCashFlowRiskOfVariability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Notional Amount, to Hedge Cash Flow Risk of Variability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotionalAmountToHedgeCashFlowRiskOfVariability_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Notional amount, to hedge the cash flow risk of variability.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotionalAmountToHedgeCashFlowRiskOfVariability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Notional amount, to hedge cash flow risk of variability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetUsefulLife_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Life (years)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetUsefulLife_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Asset, Useful Life</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_GatewayPediatricTherapyLlcMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gateway Pediatric Therapy LLC [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_GatewayPediatricTherapyLlcMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Gateway Pediatric Therapy LLC</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_GatewayPediatricTherapyLlcMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Gateway</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_GatewayPediatricTherapyLlcMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Gateway Pediatric Therapy LLC.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PaymentOfUnderwritingDiscountsAndCommissions_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Payment of underwriting discounts and commissions.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PaymentOfUnderwritingDiscountsAndCommissions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payment of Underwriting Discounts and Commissions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PaymentOfUnderwritingDiscountsAndCommissions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Underwriting discounts and commissions paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisaggregationOfRevenueTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disaggregation of Revenue [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Basic and Diluted Net Income Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Increase (Decrease) in Other Operating Assets and Liabilities, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Other Operating Assets and Liabilities, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other assets and liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other assets and liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Other assets gross.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Assets Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ConversionOfTangibleEquityUnitsIntoCommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Conversion Of Tangible Equity Units Into Common Stock, value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ConversionOfTangibleEquityUnitsIntoCommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Conversion of tangible equity units into common stock, value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ConversionOfTangibleEquityUnitsIntoCommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Conversion of tangible equity units into common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Loss per share - basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net income (loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net income per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisaggregationOfRevenueTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disaggregation of Revenue [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisaggregationOfRevenueTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Revenue by Payor Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TaxEffectOfNetShareSettlementOfEquityAwardsValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tax Effect of Net Share Settlement of Equity Awards Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TaxEffectOfNetShareSettlementOfEquityAwardsValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tax effect of net share settlement of equity awards value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TaxEffectOfNetShareSettlementOfEquityAwardsValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tax effect of net share settlement of equity awards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Long-term debt repayments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Repayments of Long-Term Debt, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Repayments of Long-Term Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Repayment of borrowings</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign currency translation adjustments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssued1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssued1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock issued in connection with acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtFinancingFeesPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt financing, fees paid.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtFinancingFeesPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Financing, Fees Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtFinancingFeesPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fees paid to arranger</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevolvingCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revolving Credit Facility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevolvingCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revolving Credit Facility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinitelivedIntangibleAssetsAcquired1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Assets Acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinitelivedIntangibleAssetsAcquired1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Intangible assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Accounts Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trade accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accounts Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Accounts receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Adjustments to reconcile net income to cash provided by operating activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TrancheB5TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tranche B 5 Term Loan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TrancheB5TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tranche B 5 term loan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TrancheB5TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tranche B- 5 Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsForNewAccountingPronouncementsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounting Standards Update [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProductConcentrationRiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Product Concentration Risk [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProductConcentrationRiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Product Concentration Risk</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MaterialReconcilingItemsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, Reconciling Item, Excluding Corporate Nonsegment [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MaterialReconcilingItemsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Material Reconciling Items</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ConsolidationItemsDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consolidation Items [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TerminationFeesPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Termination Fees Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TerminationFeesPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Termination fees paid.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TerminationFeesPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Termination fees paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tangible equity units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tangible Equity Units Text Block</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tangible Equity Units ("TEUs")</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), Reclassification, Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income tax effects of amounts reclassified to earnings</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Parent [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shareholders' equity:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PrivateAndOtherMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Private and Other.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PrivateAndOtherMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Private and Other [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PrivateAndOtherMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Private and Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Small Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Small Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityCommitmentFeeAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Commitment Fee Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityCommitmentFeeAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Line of credit, commitment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Increase (Decrease) in Accrued Liabilities, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accrued Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TwoThousandTwentySixAcquisitionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2026 Acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TwoThousandTwentySixAcquisitionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty Six Acquisition [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TwoThousandTwentySixAcquisitionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand twenty six acquisition.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketApproachValuationTechniqueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Valuation, Market Approach [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketApproachValuationTechniqueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Market Approach</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Retained Earnings (Accumulated Deficit), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings (Accumulated Deficit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Retained earnings (accumulated deficit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SwinglineLoansMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Swingline loans.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SwinglineLoansMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Swingline Loans [member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SwinglineLoansMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Swingline Loans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceInitialPublicOffering_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Proceeds from initial public offering, net of underwriting discounts and commission and offering-related expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceInitialPublicOffering_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net proceeds from offering</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceInitialPublicOffering_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from issuance of common stock on initial public offering, net</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock price per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EqualToOrLessThanFifteenPointTwoEightButGreaterThanOrEqualToThirteenPointZeroZeroMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Equal to or less than fifteen point two eight but greater than or equal to thirteen point zero zero.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EqualToOrLessThanFifteenPointTwoEightButGreaterThanOrEqualToThirteenPointZeroZeroMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equal to or Less Than Fifteen Point Two Eight but Greater Than or Equal to Thirteen Point Zero Zero [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EqualToOrLessThanFifteenPointTwoEightButGreaterThanOrEqualToThirteenPointZeroZeroMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equal to or less than $15.28 but greater than or equal to $13.00</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationAccumulatedDepreciationOfPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Accumulated Depreciation Of Property, Plant, And Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationAccumulatedDepreciationOfPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal group, including discontinued operation, accumulated depreciation of property, plant, and equipment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationAccumulatedDepreciationOfPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated depreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedInsuranceCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Insurance, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedInsuranceCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Health insurance reserves</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeDerivativesQualifyingAsHedgesNetOfTaxPeriodIncreaseDecreaseAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), after Reclassification and Tax [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeDerivativesQualifyingAsHedgesNetOfTaxPeriodIncreaseDecreaseAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash flow hedges:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienIncrementalTermLoansTranchesB2AndB3PayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">First Lien Incremental Term Loans Tranches B-2 And B-3 - Payable To Lenders At Sofr Plus Applicable Margin [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienIncrementalTermLoansTranchesB2AndB3PayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">First Lien Incremental Term Loans Tranches B-2 and B-3 - Payable to Lenders at SOFR plus Applicable Margin</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienIncrementalTermLoansTranchesB2AndB3PayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">First lien incremental term loans tranches b-2 and b-3 - payable to lenders at SOFR plus applicable margin member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DerecognitionOfRedeemableNoncontrollingInterestNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derecognition of redeemable noncontrolling interest, net of tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DerecognitionOfRedeemableNoncontrollingInterestNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derecognition Of Redeemable Noncontrolling Interest, Net Of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DerecognitionOfRedeemableNoncontrollingInterestNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Derecognition Of Redeemable Noncontrolling Interest, Net Of Tax.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ProductsAndServicesDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Product and Service [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LossContingenciesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loss Contingencies [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PharmacySolutionsAndProviderServicesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Pharmacy solutions and provider services.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PharmacySolutionsAndProviderServicesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Pharmacy Solutions And Provider Services [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PharmacySolutionsAndProviderServicesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pharmacy Solutions and Provider Services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsAmortizingNotesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tangible Equity Units Amortizing Notes [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsAmortizingNotesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tangible equity units amortizing notes.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsAmortizingNotesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortizing Notes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current assets held for sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current assets held for sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities and Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Liabilities, Redeemable Noncontrolling Interests, and Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressPostalZipCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Postal Zip Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressPostalZipCode_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, Postal Zip Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash provided by operating activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, CODM, Profit (Loss) Measure, How Used, Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Medicare C</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Medicare C [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Medicare C.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Medicare Part C</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IndefiniteLivedLicensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Indefinite Lived Licenses.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IndefiniteLivedLicensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Indefinite Lived Licenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IndefiniteLivedLicensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Licenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IndefiniteLivedLicensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Indefinite-lived Licenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedInventory_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired, Inventory, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedInventory_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Inventories</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment, net of accumulated depreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Address Line One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, Address Line One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateImmaterialEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Change in Accounting Principle, Accounting Standards Update, Immaterial Effect [true false]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateImmaterialEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accouting standards update, immaterial effect</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share [Abstract]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ConversionOfTangibleEquityUnitsIntoCommonStockShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Conversion of tangible equity units into common stock, shares</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ConversionOfTangibleEquityUnitsIntoCommonStockShare_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Conversion of tangible equity units into common stock,share.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BalanceSheetLocationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Financial Position Location, Balance [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtInstrumentConvertibleCashInstallmentPerUnit_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt instrument convertible cash installment per unit.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtInstrumentConvertibleCashInstallmentPerUnit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument Convertible Cash Installment Per Unit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtInstrumentConvertibleCashInstallmentPerUnit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash installment per unit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ExistingContractsInterestRateSwapAgreementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Existing Contracts Interest Rate Swap Agreements [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ExistingContractsInterestRateSwapAgreementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Existing contracts interest rate swap agreements.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ExistingContractsInterestRateSwapAgreementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Existing contracts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationCurrentPortionOfObligationsUnderFinancingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current portion of obligations under financing leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationCurrentPortionOfObligationsUnderFinancingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Current Portion of Obligations under Financing Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationCurrentPortionOfObligationsUnderFinancingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal Group, Including Discontinued Operation, Current Portion of Obligations under Financing Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Right-of-Use Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease right-of-use assets, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MorganStanleyMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Morgan Stanley Member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MorganStanleyMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Morgan Stanley [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MorganStanleyMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Morgan Stanley</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net Income (Loss) Attributable to Noncontrolling Interest, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Income (Loss) Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net (loss) income attributable to redeemable noncontrolling interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Net loss attributable to noncontrolling interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss attributable to noncontrolling interests included in continuing operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PrepaidInterestRateSwaps_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest rate swaps</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PrepaidInterestRateSwaps_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Prepaid interest rate swaps.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PrepaidInterestRateSwaps_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Interest Rate Swaps</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Services revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income Taxes Paid, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Taxes Paid, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income taxes, net of refunds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GrossProfit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gross Profit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GrossProfit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gross profit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsidiary, Ownership Percentage, Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Ownership interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Redeemable noncontrolling interest percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Assets [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NontradeReceivablesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Nontrade Receivables, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NontradeReceivablesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Nontrade Receivables, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NontradeReceivablesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-trade receivables</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromSalesOfBusinessAffiliateAndProductiveAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Gross proceeds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromSalesOfBusinessAffiliateAndProductiveAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Sales of Business, Affiliate and Productive Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValuationTechniqueAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Valuation Approach and Technique [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Including Exchange Rate Effect and Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net decrease in cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net increase (decrease) in cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares excluded from computation of diluted net Income per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Other Assets, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupClassificationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group Classification [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock, par value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TypeOfAdoptionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounting Standards Update [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business combination recognized identifiable assets acquired and liabilities assumed accrued expenses.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Accrued Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MonitoringAndAdvisoryFees_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Monitoring and advisory fees.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MonitoringAndAdvisoryFees_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Monitoring and Advisory Fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MonitoringAndAdvisoryFees_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Recognized monitoring and advisory fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WorkersCompensationLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Workers' Compensation Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WorkersCompensationLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Workers compensation insurance reserves</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DefiniteLivedLicensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Definite-lived Licenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DefiniteLivedLicensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Definite-lived licenses.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DefiniteLivedLicensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Definite-lived Licenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MarchTwoThousandTwentySixOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">March Two Thousand Twenty Six Offering [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MarchTwoThousandTwentySixOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">March two thousand twenty six offering.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MarchTwoThousandTwentySixOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">March 2026 Offering</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercise of stock options, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercises in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Derivative Instruments [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Interest Rate Swap with Notional Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeNotionalAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total notional value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeNotionalAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative, Notional Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeNotionalAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Derivative, notional amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total accrued expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, Restricted Stock Award, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock for settlement of RSUs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForLegalSettlements_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Paid settlement amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForLegalSettlements_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments for Legal Settlements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_OwnershipDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Ownership [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current Fiscal Year End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current Fiscal Year End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Long-Term Debt Instruments [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfBusinessesAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Number of Businesses Acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfBusinessesAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of businesses acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedChecksInExcessOfCashBalanceCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Carrying value as of the balance sheet date of obligations incurred and payable for accrued checks in excess of cash balance current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedChecksInExcessOfCashBalanceCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Checks In Excess Of Cash Balance Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedChecksInExcessOfCashBalanceCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Checks in excess of cash balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentQuarterlyReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Quarterly Report</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherNoncurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherNoncurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired, Other Asset, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CustomerRelationshipsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Customer Relationships [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CustomerRelationshipsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Customer Relationships</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DepreciationAndAmortizationExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation and Amortization Expenses not Allocated at Segment Level</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DepreciationAndAmortizationExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Depreciation and amortization expenses not allocated at segment level.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DepreciationAndAmortizationExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation and amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, State or Province</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, State or Province</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Redeemable Noncontrolling Interest [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Remaining Borrowing Capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Line of credit facility, remaining borrowing capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_GainLossOnDispositionOfRealEstateDiscontinuedOperationsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) On Disposition Of Real Estate Discontinued Operations, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_GainLossOnDispositionOfRealEstateDiscontinuedOperationsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Gain (loss) on disposition of real estate discontinued operations, net.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_GainLossOnDispositionOfRealEstateDiscontinuedOperationsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net gain on sale of discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancialLiabilitiesFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Financial Liabilities Fair Value Disclosure, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancialLiabilitiesFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financial Liabilities Fair Value Disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancialLiabilitiesFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Financial liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancialLiabilitiesFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Financial liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Preferred Stock, Shares Outstanding, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Preferred Stock, Shares Outstanding, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred Stock, shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Comprehensive income attributable to BrightSpring Health Services, Inc. and subsidiaries</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Discontinued Operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Groups, Including Discontinued Operations, Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Long-term liabilities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-term Liabilities [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Long-Term Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConversionOfStockSharesConverted1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Conversion of Stock, Shares Converted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConversionOfStockSharesConverted1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Units converted at holder's option</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableInterestEntityOwnershipPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Variable Interest Entity, Qualitative or Quantitative Information, Ownership Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableInterestEntityOwnershipPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Ownership interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_StockRepurchasedDuringPeriodValues_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Share repurchase</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_StockRepurchasedDuringPeriodValues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Repurchased During Period Values</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_StockRepurchasedDuringPeriodValues_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Stock repurchased during period values.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Equity, Attributable to Noncontrolling Interest, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Equity, Attributable to Noncontrolling Interest, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Equity, Attributable to Noncontrolling Interest, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Noncontrolling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationLiabilityClassifiedNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Compensation Liability, Classified, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationLiabilityClassifiedNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationLiabilityClassifiedNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Deferred Compensation Liability, Classified, Noncurrent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationLiabilityClassifiedNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Deferred compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CompensatedAbsencesLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Compensated Absences Liability, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CompensatedAbsencesLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Compensated Absences Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CompensatedAbsencesLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Compensated absences</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CashFlowsFromDiscontinuedOperationsInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash flows from discontinued operations investing activities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CashFlowsFromDiscontinuedOperationsInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cash flows from discontinued operations investing activities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CashFlowsFromDiscontinuedOperationsInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash flows used in investing activities of discontinued operations:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, Stock Options Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercise of stock options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationAndAmortizationDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation and Amortization, Discontinued Operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationAndAmortizationDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation and amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AlternateBaseRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Alternate base rate.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AlternateBaseRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Alternate Base Rate [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AlternateBaseRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ABR</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsPerBasicShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations, Per Basic Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsPerBasicShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Continuing operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Income Tax Assets, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred income taxes, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Event</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredRevenueCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Deferred Revenue, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredRevenueCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Revenue, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredRevenueCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Assets, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsPrepaidExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired, Prepaid Expense and Other Asset, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsPrepaidExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NumberOfBranchesAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number Of Branches Acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NumberOfBranchesAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of branches acquired.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NumberOfBranchesAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of branches acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">AOCI Attributable to Parent [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Other Comprehensive Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SummaryOfSignificantAccountingPolicyTable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Summary of significant accounting policy.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SummaryOfSignificantAccountingPolicyTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Summary Of Significant Accounting Policy [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Assets, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Disposal Group, Including Discontinued Operation, Assets, Noncurrent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-current assets held for sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Consideration Transferred</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Consideration transferred to asset acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Aggregate purchase price, net of cash acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Value, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, $0.01 par value, 250,000,000 authorized, no shares issued and outstanding at March 31, 2026 and December 31, 2025</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Intangible Assets, Other than Goodwill, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Excluding Goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Intangible assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Groups, Including Discontinued Operations [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDisposalGroupsIncludingDiscontinuedOperationsIncomeStatementBalanceSheetAndAdditionalDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of the Reconciles the Gross Proceeds on Sale, the Financial Results, Aggregate Carrying Amounts of Assets and Liabilities Held for Sale and Significant Non-cash Items and Purchases of Property and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Selling, General and Administrative Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Selling, General and Administrative Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Selling, general, and administrative expenses not allocated at segment level</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Selling, general, and administrative expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Maturity Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maturity date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Line of credit facility, maturity date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Minimum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Minimum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancialInstrumentAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financial Instrument [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current assets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLongTermInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other investments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLongTermInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Long-Term Investments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AmortizationOfIntangibleAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amortization of Intangible Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AmortizationOfIntangibleAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortization expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 3 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Level 3</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Financial Assets or Liabilities Recorded at Fair value on Recurring Basis</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsIssuedDuringPeriodNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tangible Equity Units Issued During Period New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsIssuedDuringPeriodNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tangible Equity Units Issued During Period New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsIssuedDuringPeriodNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tangible equity unit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProductMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Product [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProductMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Products</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedLiabilitiesCurrentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accrued liabilities current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedLiabilitiesCurrentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Liabilities Current [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedLiabilitiesCurrentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IncomeTaxExpenseBenefitExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Expense (Benefit) Expenses not Allocated at Segment Level</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IncomeTaxExpenseBenefitExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Income tax expense (benefit) expenses not allocated at segment level.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_IncomeTaxExpenseBenefitExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income tax expense (benefit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transactions [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationPlanAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Compensation Plan Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationPlanAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accounts Receivable, after Allowance for Credit Loss, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Receivable, after Allowance for Credit Loss, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts receivable, net of allowance for credit losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LcFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">LC facility member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LcFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">LC Facility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LcFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">LC Facility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_GreaterThanFifteenPointTwoEightMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Greater than fifteen point two right.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_GreaterThanFifteenPointTwoEightMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Greater Than Fifteen Point Two Eight [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_GreaterThanFifteenPointTwoEightMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Greater than $15.28</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ScheduleOfIntangibleAssetsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule Of Intangible Assets.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ScheduleOfIntangibleAssetsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Intangible Assets [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Liabilities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PrepaidMaintenance_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Prepaid maintenance.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PrepaidMaintenance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Maintenance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PrepaidMaintenance_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid maintenance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Shares issued for payment of acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Shares Issued, Shares, Share-Based Payment Arrangement, after Forfeiture, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares Issued, Shares, Share-Based Payment Arrangement, after Forfeiture</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares issued under share-based compensation plan, including tax effects, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeDescriptionOfTerms_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative, Description of Terms</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeDescriptionOfTerms_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative, description of terms</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillPurchaseAccountingAdjustments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Measurement period adjustments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillPurchaseAccountingAdjustments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill, Measurement Period Adjustment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Basis spread on variable rate (as a percent)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Basis Spread on Variable Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfGoodwillTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Goodwill [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfGoodwillTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Changes to Goodwill, by Reportable Segment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskByBenchmarkAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Benchmark [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNoncurrentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt Issuance Costs, Noncurrent, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNoncurrentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Issuance Costs, Noncurrent, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNoncurrentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred debt issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Variable Interest Entity, Primary Beneficiary [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Primary Beneficiary</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current portion of obligations under financing leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EarningsPerShareTable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Earnings per share.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EarningsPerShareTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings per Share [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedGeneralAndProfessionalLiabilityInsuranceReservesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Carrying value as of the balance sheet date of obligations incurred and payable for accrued general and professional liability insurance reserves current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedGeneralAndProfessionalLiabilityInsuranceReservesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued General And Professional Liability Insurance Reserves Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedGeneralAndProfessionalLiabilityInsuranceReservesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">General and professional liability insurance reserves</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OctoberTwoThousandTwentyFiveOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">October 2025 Offering</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OctoberTwoThousandTwentyFiveOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">October Two Thousand Twenty Five Offering [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OctoberTwoThousandTwentyFiveOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">October Two Thousand Twenty Five Offering [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalExpendituresIncurredButNotYetPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Capital Expenditures Incurred but Not yet Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalExpendituresIncurredButNotYetPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchases of property and equipment in accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net (loss) income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current liabilities held for sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current liabilities held for sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ScheduleOfProceedsFromIssuanceOfTangibleEquityUnitsAllocatedToEquityAndDebtTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule of proceeds from issuance of tangible equity units allocated to equity and debt.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ScheduleOfProceedsFromIssuanceOfTangibleEquityUnitsAllocatedToEquityAndDebtTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Proceeds from Issuance of Tangible Equity Units Allocated to Equity and Debt [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ScheduleOfProceedsFromIssuanceOfTangibleEquityUnitsAllocatedToEquityAndDebtTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Proceeds from Issuance Allocated to Equity and Debt Based on Relative Fair Value of each TEU</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedLegalSettlementsAndProfessionalFeesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Carrying value as of the balance sheet date of obligations incurred through that date and payable accrued legal settlements and professional fees current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedLegalSettlementsAndProfessionalFeesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Legal Settlements And Professional Fees Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedLegalSettlementsAndProfessionalFeesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Legal settlements and professional fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MizuhoCapitalMarketsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Mizuho Capital Markets [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MizuhoCapitalMarketsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Mizuho Capital Markets.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MizuhoCapitalMarketsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Mizuho Capital Markets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongtermDebtTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LossContingenciesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loss Contingencies [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average shares outstanding - basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted Average Number of Shares Outstanding, Basic, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAcquiredDuringPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill, Acquired During Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAcquiredDuringPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Goodwill added through acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Liability Assumed, Liability, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Business Combination, Recognized Liability Assumed, Liability, Noncurrent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_StockRepurchasedDuringPeriodShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Repurchased During Period Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_StockRepurchasedDuringPeriodShare_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Stock repurchased during period share.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_StockRepurchasedDuringPeriodShare_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Share repurchase, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentInformationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Information [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TrancheB2TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tranche B-2 Term Loan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TrancheB2TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tranche B-2 Term Loan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TrancheB2TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tranche B-2 Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesCurrentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term Liabilities Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesCurrentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long Term Liabilities Current [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesCurrentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Long term liabilities current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityOther_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityOther_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stockholders' Equity, Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityOther_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPlanModificationIncrementalCompensationCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Plan Modification, Incremental Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPlanModificationIncrementalCompensationCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Incremental share-based compensation expense recognized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Effective Income Tax Rate Reconciliation [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Reconciliation of Effective Tax Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations, Net of Tax, Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net income (loss) from continuing operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net income from continuing operations attributable to common shareholders</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseRight-Of-UseAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Operating Lease Right-of-Use Assets, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseRight-Of-UseAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal Group, Including Discontinued Operation, Operating Lease Right-of-Use Assets, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseRight-Of-UseAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease right-of-use assets, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CommonStockSharesPurchased_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock shares purchased from underwriter</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CommonStockSharesPurchased_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock Shares Purchased</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CommonStockSharesPurchased_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Common stock shares purchased.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementBusinessSegmentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segments [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationIncomeLossFromDiscontinuedOperationBeforeIncomeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operation, Income (Loss) from Discontinued Operation, before Income Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationIncomeLossFromDiscontinuedOperationBeforeIncomeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income of discontinued operations before incomes taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationIncomeLossFromDiscontinuedOperationBeforeIncomeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income from discontinued operations, net of income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Events</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Events [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total long-term debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total debt, net of debt issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transactions Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related Party Transactions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredTaxLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred income taxes, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationDeferredTaxLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Deferred Tax Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableRateDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Variable Rate [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Equity, Attributable to Parent, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Equity, Attributable to Parent, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total shareholders' equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred Stock , par value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Basis of Accounting, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Basis of Presentation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Stockholders' Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOperatingLeaseRightOfUseAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business combination recognized identifiable assets acquired and liabilities assumed operating lease right-of-use assets.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOperatingLeaseRightOfUseAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Operating Lease Right-of-use Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOperatingLeaseRightOfUseAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease right-of-use assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestByLegalEntityTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Redeemable Noncontrolling Interest [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CommonStockPreferredStockAndShareBasedCompensationTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Common stock, preferred stock, and share-based compensation.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CommonStockPreferredStockAndShareBasedCompensationTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Preferred Stock, and Share-Based Compensation [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CommonStockPreferredStockAndShareBasedCompensationTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock, Preferred Stock, and Share-Based Compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityMethodInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Method Investments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityMethodInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity method investments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValuationTechniqueDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Valuation Approach and Technique [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Other.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UseOfEstimates_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Use of Estimates, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UseOfEstimates_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Use of Estimates</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Property, Plant, and Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired, Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Disclosures [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_GeneralAndProfessionalLiabilityInsuranceReservesLongTermLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Carrying value as of the balance sheet date of general and professional liability insurance reserves long-term liabilities, noncurrent (with maturities initially due after one year or beyond the operating cycle if longer), excluding current portion.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_GeneralAndProfessionalLiabilityInsuranceReservesLongTermLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">General And Professional Liability Insurance Reserves Long-term Liabilities, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_GeneralAndProfessionalLiabilityInsuranceReservesLongTermLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">General and professional liability insurance reserves</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DistributionOfFundCovid19_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Distribution of fund covid19.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DistributionOfFundCovid19_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Distribution Of Fund Covid19</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DistributionOfFundCovid19_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fund authorized to be distributed to health care providers</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProductInformationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Product Information [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncontrollingInterestMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncontrolling Interest [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncontrollingInterestMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SummaryOfSignificantAccountingPolicyLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Summary of significant accounting policy.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SummaryOfSignificantAccountingPolicyLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Summary Of Significant Accounting Policy [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SharesWithheldRelatedToNetShareSettlementValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares Withheld Related To Net Share Settlement Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SharesWithheldRelatedToNetShareSettlementValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Shares withheld related to net share settlement value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SharesWithheldRelatedToNetShareSettlementValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares withheld related to net share settlement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Accrued Liabilities [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Accrued Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPerShareWeightedAveragePriceOfSharesPurchased_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Per Share Weighted Average Price of Shares Purchased</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPerShareWeightedAveragePriceOfSharesPurchased_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">VWAP of BTSG Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPerShareWeightedAveragePriceOfSharesPurchased_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Average applicable market value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentPeriodicPayment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt Instrument, Periodic Payment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentPeriodicPayment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Periodic Payment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentPeriodicPayment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">TEU installment payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Liabilities, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, CODM, Individual Title and Position or Group Name [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerBasicShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Discontinued Operations and Disposal of Discontinued Operations, Net of Tax, Per Basic Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerBasicShare_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income (Loss) from Discontinued Operations and Disposal of Discontinued Operations, Net of Tax, Per Basic Share, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerBasicShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Plan Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NumberOfCustomer_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of Customer.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NumberOfCustomer_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Customer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NumberOfCustomer_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of customer whose revenue was 10% or more of consolidated revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PharmacySolutionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Pharmacy Solutions.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PharmacySolutionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Pharmacy Solutions [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PharmacySolutionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pharmacy Solutions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Interest expense, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpense_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Interest expense, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Expense, Operating and Nonoperating</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest expense, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Temporary Equity, Carrying Amount, Including Portion Attributable to Noncontrolling Interests, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Temporary Equity, Carrying Amount, Including Portion Attributable to Noncontrolling Interests, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Temporary Equity, Carrying Amount, Including Portion Attributable to Noncontrolling Interests, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, Including Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable noncontrolling interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Facility [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfGoodsAndServicesSold_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cost of Goods and Services Sold, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfGoodsAndServicesSold_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cost of Product and Service Sold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfGoodsAndServicesSold_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cost of goods and services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfGoodsAndServicesSold_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Cost of services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromRepaymentsOfLinesOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from (Repayments of) Lines of Credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromRepaymentsOfLinesOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Repayments of the Revolving Credit Facility, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOfLongLivedAssetsHeldForUse_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Impairment, Long-Lived Asset, Held-for-Use, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOfLongLivedAssetsHeldForUse_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Impairment, Long-Lived Asset, Held-for-Use</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOfLongLivedAssetsHeldForUse_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Impairment of long-lived assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ChangeInFairValueOfContingentConsiderationsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Change in fair value of contingent considerations net.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ChangeInFairValueOfContingentConsiderationsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Change in fair value of contingent consideration, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ChangeInFairValueOfContingentConsiderationsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Change in Fair Value of Contingent Considerations Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationCurrentPortionOfObligationsUnderOperatingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Current Portion of Obligations under Operating Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationCurrentPortionOfObligationsUnderOperatingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal Group, Including Discontinued Operation, Current Portion of Obligations under Operating Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationCurrentPortionOfObligationsUnderOperatingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current portion of obligations under operating leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related and Nonrelated Parties [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, City or Town</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, City or Town</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsPurchaseContractsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tangible Equity Units Purchase Contracts [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsPurchaseContractsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tangible equity units purchase contracts.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsPurchaseContractsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchase Contracts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Intangible Assets, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationIntangibleAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Intangible assets, net of accumulated amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateCashFlowHedgeAssetAtFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Cash Flow Hedge Asset at Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateCashFlowHedgeAssetAtFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair value of interest rate swaps asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Reportable Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of reportable segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Security Exchange Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Security Exchange Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Facility [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Indefinite-Lived Intangible Assets (Excluding Goodwill), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Indefinite-Lived Intangible Assets (Excluding Goodwill), Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Indefinite-Lived Intangible Assets (Excluding Goodwill), Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Indefinite-Lived Intangible Assets (Excluding Goodwill)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Indefinite-lived assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Redeemable Noncontrolling Interest, Equity, Carrying Amount, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Redeemable Noncontrolling Interest, Equity, Carrying Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable non-controlling interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredOfferingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Offering Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredOfferingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred offering costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_CounterpartyNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Counterparty Name [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income from continuing operations before income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockIncludingAdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock Including Additional Paid in Capital [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockIncludingAdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional Paid-In Capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Discontinued Operations, Net of Tax, Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net income from discontinued operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income from discontinued operations, net of income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CompensationRelatedCostsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Compensation Related Costs [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CompensationRelatedCostsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Compensation Related Costs [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities, Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RevolvingCreditLoansPayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revolving Credit Loans - Payable To Lenders At Sofr Plus Applicable Margin [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RevolvingCreditLoansPayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revolving Credit Loans - Payable to Lenders at SOFR plus Applicable Margin</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RevolvingCreditLoansPayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Revolving credit loans - payable to lenders at SOFR plus applicable margin member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerDilutedShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Discontinued Operations and Disposal of Discontinued Operations, Net of Tax, Per Diluted Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerDilutedShare_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income (Loss) from Discontinued Operations and Disposal of Discontinued Operations, Net of Tax, Per Diluted Share, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerDilutedShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InventoryNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Inventory, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InventoryNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Inventory, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InventoryNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Inventories</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Cash and cash equivalents at end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Cash and cash equivalents at beginning of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash and cash equivalents included in continuing operations at end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash and cash equivalents included in continuing operations at end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Paid, Excluding Capitalized Interest, Operating Activity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Period End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Period End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LossOnExtinguishmentOfDebtExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loss on extinguishment of debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LossOnExtinguishmentOfDebtExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loss on Extinguishment of Debt Expenses not Allocated at Segment Level</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LossOnExtinguishmentOfDebtExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Loss on extinguishment of debt expenses not allocated at segment level.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesAutomobileInsuranceReservesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Carrying value as of the balance sheet date of long-term liabilities automobile insurance reserves, noncurrent (with maturities initially due after one year or beyond the operating cycle if longer), excluding current portion.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesAutomobileInsuranceReservesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-term Liabilities Automobile Insurance Reserves, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesAutomobileInsuranceReservesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Automobile insurance reserves</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TwentySeventeenStockPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Twenty seventeen stock plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TwentySeventeenStockPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Twenty Seventeen Stock Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TwentySeventeenStockPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2017 Stock Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CostOfServices_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cost of services.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CostOfServices_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cost of services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RelatedPartyTransactionsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transactions [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RelatedPartyTransactionsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disclosure of accounting policy for related party transactions.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RelatedPartyTransactionsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related Party Transactions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DuesAndSubscriptions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Dues And Subscriptions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DuesAndSubscriptions_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Dues and subscriptions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DuesAndSubscriptions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Dues and subscriptions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtInstrumentFloorRate_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt instrument floor rate.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtInstrumentFloorRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument Floor Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtInstrumentFloorRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument, floor rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Acquired Finite-Lived Intangible Assets, Weighted Average Useful Life</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Definite-lived intangible assets estimated weighted average useful life</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfFinancialPositionAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Financial Position [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedStockUnitsRSUMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restricted Stock Units (RSUs) [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedStockUnitsRSUMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">RSUs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Assets, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current assets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_HarvestGroveLTCLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Harvest Grove</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_HarvestGroveLTCLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Harvest Grove L T C L L C [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_HarvestGroveLTCLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Harvest Grove ITC LLC.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_HarvestGroveLTCLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Harvest Grove LTC, LLC</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementClassOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ComprehensiveIncomeLossNetOfTaxAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Comprehensive income (loss), net of tax, attributable to redeemable noncontrolling interest.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ComprehensiveIncomeLossNetOfTaxAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income Loss Attributable To Redeemable Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ComprehensiveIncomeLossNetOfTaxAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Comprehensive (loss) income attributable to redeemable noncontrolling interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ComprehensiveIncomeLossNetOfTaxAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Comprehensive loss attributable to redeemable noncontrolling interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CostOfGoods_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cost of goods.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CostOfGoods_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cost of goods</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PercentageOfEbitdaPayableAsAdvisoryFee_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage of EBITDA Payable as Advisory Fee</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PercentageOfEbitdaPayableAsAdvisoryFee_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of EBITDA payable as advisory fee</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PercentageOfEbitdaPayableAsAdvisoryFee_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of EBITDA payable as advisory fee.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financial Instruments [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Cash and Cash Equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PaymentsForUnderwritingDiscountsAndCommissions_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net of underwriting discounts and commissions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PaymentsForUnderwritingDiscountsAndCommissions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net of underwriting fees and offering costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PaymentsForUnderwritingDiscountsAndCommissions_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Payments for underwriting discounts and commissions.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PaymentsForUnderwritingDiscountsAndCommissions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments For Underwriting Discounts And Commissions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityRedemptionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Redeemable Noncontrolling Interest, Equity, Redemption Value, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityRedemptionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Redeemable Noncontrolling Interest, Equity, Redemption Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityRedemptionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemed noncontrolling interest Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Groups, Including Discontinued Operations [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableRateAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Variable Rate [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Indefinite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Finite-Lived Intangible Assets, Gross, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Assets, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Definite-lived assets, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumAmountOutstandingDuringPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Maximum Amount Outstanding During Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumAmountOutstandingDuringPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate amount of outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CertainPostClosingAdjustments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Certain Post closing Adjustments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CertainPostClosingAdjustments_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Certain post closing adjustments.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CertainPostClosingAdjustments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less: certain post-closing adjustments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average shares outstanding - diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted Average Number of Shares Outstanding, Diluted, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFileNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Securities Act File Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFileNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity File Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfFinancialPositionLocationActivityCapitalizationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Financial Position Location, Activity, Capitalization [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationOtherReconcilingItemsPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Other Reconciling Items, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationOtherReconcilingItemsPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Discrete items recognized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CoverAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cover [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DirectCostsToSell_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Direct Costs To Sell</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DirectCostsToSell_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Direct costs to sell.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DirectCostsToSell_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less: direct costs to sell</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentPortionOfObligationsUnderFinancingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current portion of obligations under financing leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentPortionOfObligationsUnderFinancingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Current Portion Of Obligations Under Financing Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentPortionOfObligationsUnderFinancingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Current Portion Of Obligations Under Financing Leases.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationObligationsUnderOperatingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Obligations under Operating Leases, Net of Current Portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationObligationsUnderOperatingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal Group, Including Discontinued Operation, Obligations under Operating Leases, Net of Current Portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationObligationsUnderOperatingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Obligations under operating leases, net of current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalBalanceSheetDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Supplemental Balance Sheet Disclosures [Text Block]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WorkersCompensationLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Workers' Compensation Liability, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WorkersCompensationLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Workers compensation insurance reserves</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SalesRevenueNetMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue Benchmark [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SalesRevenueNetMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CreditAgricoleCorporateAndInvestmentBankOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Agricole Corporate And Investment Bank One [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CreditAgricoleCorporateAndInvestmentBankOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Credit agricole corporate and investment bank one.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CreditAgricoleCorporateAndInvestmentBankOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Credit Agricole Corporate and Investment Bank</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock [Domain]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment Information</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TwoThousandTwentyFiveAcquisitionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty Five Acquisition [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TwoThousandTwentyFiveAcquisitionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand twenty five acquisition.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Contingent Consideration, Liability, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Contingent consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesAcquisitions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares issued for payment of acquisition, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesAcquisitions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, Acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Pro Forma Information, Pro Forma Income (Loss), after Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net income from continuing operations attributable to BrightSpring Health Services, Inc. and subsidiaries</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trade accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Liability Assumed, Accounts Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Pro Forma Information [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Finite-Lived Intangible Assets, Net, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Finite-Lived Intangible Assets, Net, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Assets, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total intangible assets, Net Carrying Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ExtinguishmentOfRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Extinguishment of redeemable noncontrolling interest.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ExtinguishmentOfRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Extinguishment Of Redeemable Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ExtinguishmentOfRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Extinguishment of redeemable noncontrolling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ExtinguishmentOfRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Extinguishment of redeemable noncontrolling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntangibleAssetsGrossExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Intangible Assets, Gross (Excluding Goodwill), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntangibleAssetsGrossExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Assets, Gross (Excluding Goodwill)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntangibleAssetsGrossExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total intangible assets, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gain (Loss) on Extinguishment of Debt, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) on Extinguishment of Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loss on debt extinguishment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Loss on extinguishment of debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_WeightedAveragePricePerPurchaseContract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Weighted average price per purchase contract.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_WeightedAveragePricePerPurchaseContract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted average price per purchase contract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_WeightedAveragePricePerPurchaseContract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average price per purchase contract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_WeightedAveragePricePerPurchaseContract_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Average applicable market value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsDisposalGroupIncludingDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash and cash equivalents included in assets held for sale at end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsDisposalGroupIncludingDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfProductInformationTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Nature of Operation, Product Information, Concentration of Risk [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative, Term of Contract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative, maturity term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Recently Adopted and Issued Accounting Standards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Recently Adopted Accounting Standards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TradeReceivablesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trade Receivables</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TradeReceivablesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Trade receivables.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TradeReceivablesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Trade Receivables [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDispositionOfAssets1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) on Disposition of Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDispositionOfAssets1_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gain (Loss) on Disposition of Assets, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDispositionOfAssets1_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Loss (gain) on disposition of fixed assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_OwnershipAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Ownership [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SHCMedicalPartnersLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Abode Care Partners</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SHCMedicalPartnersLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">S H C Medical Partners L L C [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SHCMedicalPartnersLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">SHC Medical Partners LLC.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesNoncurrentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Long term liabilities noncurrent.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesNoncurrentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long Term Liabilities Noncurrent [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesNoncurrentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InsuranceReceivableForMalpracticeNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Insurance Receivable for Malpractice, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InsuranceReceivableForMalpracticeNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Insurance recoveries</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash receivable for the disposal including discontinued operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Common Stock, Shares, Outstanding, Ending Balance</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Current</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentTransitionReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Transition Report</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipmentNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment, net of accumulated depreciation of $104,314</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ProfitLossExcludingRedeemableNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net income</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments for Repurchase of Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Repurchase of shares of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Repurchase of shares of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncompeteAgreementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncompete Agreements [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncompeteAgreementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Covenants Not to Compete</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income (Loss), Net of Tax, Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total comprehensive income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfCashFlowsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Cash Flows [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_UnderwriterArrangerAndTransactionFees_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Underwriter Arranger And Transaction Fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_UnderwriterArrangerAndTransactionFees_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Underwriter arranger and transaction fees.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_UnderwriterArrangerAndTransactionFees_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Underwriter, arranger and transaction fees paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CostOfDrugs_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cost of drugs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CostOfDrugs_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cost of Drugs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CostOfDrugs_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cost of drugs.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock on initial public offering, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Payments to Acquire Businesses, Net of Cash Acquired, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Businesses, Net of Cash Acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Acquisitions of businesses, net of cash acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Acquisitions of businesses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateSwapMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Swap [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateSwapMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest Rate Swaps</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessAcquisitionCostOfAcquiredEntityTransactionCosts1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Transaction costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessAcquisitionCostOfAcquiredEntityTransactionCosts1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Acquisition Cost Of Acquired Entity Transaction Costs 1</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessAcquisitionCostOfAcquiredEntityTransactionCosts1_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business acquisition cost of acquired entity transaction costs 1.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Earnings Per Share ("EPS")</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Balance, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Balance, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationsHeldForSaleOrDisposedOfBySaleMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operations, Held-for-Sale or Disposed of by Sale [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationsHeldForSaleOrDisposedOfBySaleMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Discontinued Operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operations and Disposal Groups [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net income attributable to BrightSpring Health Services, Inc. and subsidiaries</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TerminationFees_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Termination Fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TerminationFees_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Termination fees.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TerminationFees_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Termination fees paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_InterestRateSwapsNonCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest rate swaps</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_InterestRateSwapsNonCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Swaps Non-current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_InterestRateSwapsNonCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Interest rate swaps non-current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SwinglineLoansAndBaseRateLoans-PayableToLendersAtABRPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Swingline Loans and Base Rate Loans - Payable to Lenders at ABR Plus Applicable Margin [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SwinglineLoansAndBaseRateLoans-PayableToLendersAtABRPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Swingline Loans and Base Rate Loans - Payable to Lenders at ABR Plus Applicable Margin.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SwinglineLoansAndBaseRateLoans-PayableToLendersAtABRPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Swingline Loans and Base Rate Loans - Payable to Lenders at ABR Plus Applicable Margin</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInInventories_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Increase (Decrease) in Inventories, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInInventories_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Inventories</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInInventories_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Inventories</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInInventories_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Inventories</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DepreciationAndAmortizationExpenseFromReportableSegment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment depreciation and amortization expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DepreciationAndAmortizationExpenseFromReportableSegment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation And Amortization Expense From Reportable Segment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DepreciationAndAmortizationExpenseFromReportableSegment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Depreciation and amortization expense from reportable segment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsAttributableToNoncontrollingEntity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less: Net loss attributable to noncontrolling interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsAttributableToNoncontrollingEntity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations, Net of Tax, Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsAttributableToNoncontrollingEntity_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: Net loss attributable to noncontrolling interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Assets, Net (Excluding Goodwill)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Intangible assets, net of accumulated amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Total intangible assets, Net Carrying Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Intangible assets, net of accumulated amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrual for Taxes Other than Income Taxes, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Taxes other than income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RedemptionOfNoncontrollingInterestPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Redemption of noncontrolling interest percentage.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RedemptionOfNoncontrollingInterestPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Redemption of Noncontrolling Interest Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RedemptionOfNoncontrollingInterestPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemed noncontrolling interest percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinesses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Divestiture of Businesses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinesses_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Proceeds from sale of discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinesses_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Definitive agreement for cash proceeds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Prepaid Expense and Other Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicaidMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Medicaid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicaidMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Medicaid.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicaidMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Medicaid [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Year Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Fiscal Year Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Exercise Price Range [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NumberOfTangibleEquityUnitsIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of tangible equity units issued.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NumberOfTangibleEquityUnitsIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Tangible Equity Units Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NumberOfTangibleEquityUnitsIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tangible equity units issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CarryingAmountOfCommunityLivingBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Carrying Amount Of Community Living Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CarryingAmountOfCommunityLivingBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Carrying amount of community living business.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CarryingAmountOfCommunityLivingBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less: carrying amount of Community Living business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskBenchmarkDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Benchmark [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessAcquisitionNumberOfBranches_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Acquisition Number Of Branches</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessAcquisitionNumberOfBranches_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business acquisition number of branches.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessAcquisitionNumberOfBranches_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of branches</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investing activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accounts Payable, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trade accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienPayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">First Lien - Payable To Lenders At Sofr Plus Applicable Margin [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienPayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">First Lien - Payable to Lenders at SOFR plus Applicable Margin</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_FirstLienPayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">First lien - payable to lenders at SOFR plus applicable margin member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ThresholdAmountToDetermineCommonStockIssuance_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Threshold amount to determine common stock issuance.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ThresholdAmountToDetermineCommonStockIssuance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Threshold Amount to Determine Common Stock Issuance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ThresholdAmountToDetermineCommonStockIssuance_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amount to determine Common Stock Issuance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeMaturityDates_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative, Contract End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeMaturityDates_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative, maturity date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Costs, Capitalized, Prepaid, and Other Assets Disclosure [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Prepaid Expenses and Other Current Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Shares Issued, Value, Share-Based Payment Arrangement, after Forfeiture, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares Issued, Value, Share-Based Payment Arrangement, after Forfeiture</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares issued under share-based compensation plan, including tax effects</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestDecreaseFromRedemptions_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Purchase of redeemable noncontrolling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestDecreaseFromRedemptions_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Purchase of redeemable noncontrolling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestDecreaseFromRedemptions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Redeemed noncontrolling interest Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestDecreaseFromRedemptions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchase of noncontrolling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CreditAgricoleCorporateAndInvestmentBankMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Credit Agricole Corporate And Investment Bank Member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CreditAgricoleCorporateAndInvestmentBankMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Agricole Corporate And Investment Bank [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CreditAgricoleCorporateAndInvestmentBankMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Credit Agricole Corporate and Investment Bank</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherDirectCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Direct Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherDirectCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Other direct costs.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherDirectCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other direct costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EarningsBeforeInterestIncomeTaxesDepreciationAndAmortizationFromReportableSegment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Earnings before interest income taxes depreciation and amortization from reportable segment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EarningsBeforeInterestIncomeTaxesDepreciationAndAmortizationFromReportableSegment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Before Interest Income Taxes Depreciation And Amortization From Reportable Segment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EarningsBeforeInterestIncomeTaxesDepreciationAndAmortizationFromReportableSegment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment EBITDA</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EarningsBeforeInterestIncomeTaxesDepreciationAndAmortizationFromReportableSegment_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Total Segment EBITDA</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TrancheB3TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tranche B-3 Term Loan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TrancheB3TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tranche B-3 Term Loan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TrancheB3TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tranche B-3 Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DeferredIncomeTaxesExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Income Taxes Expense (Benefit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DeferredIncomeTaxesExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Deferred income taxes expense (benefit).</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DeferredIncomeTaxesExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred income taxes, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfOtherAssetsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Other Assets [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfOtherAssetsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Other Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationIncomeLossFromDiscontinuedOperationNetOfTaxPerDilutedShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operation, Income (Loss) from Discontinued Operation, Net of Tax, Per Diluted Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationIncomeLossFromDiscontinuedOperationNetOfTaxPerDilutedShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Disclosures [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherPrepaidExpensesAndCurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Other prepaid expenses and current assets.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherPrepaidExpensesAndCurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Prepaid Expenses and Current Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_OtherPrepaidExpensesAndCurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other prepaid expenses and current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueAcquisitions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares issued for payment of acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueAcquisitions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, Acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ServiceFees_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Service fees.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ServiceFees_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Service Fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ServiceFees_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Service fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedPropertyInsuranceReserves_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Property Insurance Reserves</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedPropertyInsuranceReserves_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accrued property insurance reserves.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedPropertyInsuranceReserves_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property insurance reserves</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationInterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Interest Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationInterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest expense, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss attributable to common shareholders</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net income attributable to common shareholders</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities held for sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Borrowings outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Line of Credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Long-Term Line of Credit, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionsProFormaIncomeLossFromContinuingOperationsBeforeChangesInAccountingAndExtraordinaryItemsNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Pro Forma Information, Pro Forma Income (Loss) from Continuing Operations, after Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionsProFormaIncomeLossFromContinuingOperationsBeforeChangesInAccountingAndExtraordinaryItemsNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Operating income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionsProFormaIncomeLossFromContinuingOperationsBeforeChangesInAccountingAndExtraordinaryItemsNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionProFormaInformationTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Pro Forma Information [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionProFormaInformationTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Unaudited Pro Forma Consolidated Financial Information</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInstrumentRiskAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Instrument [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ConsiderationForPurchaseOfRedeemableNoncontrollingInterestInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Consideration for purchase of redeemable noncontrolling interest in accounts payable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ConsiderationForPurchaseOfRedeemableNoncontrollingInterestInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consideration For Purchase Of Redeemable Noncontrolling Interest In Accounts Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ConsiderationForPurchaseOfRedeemableNoncontrollingInterestInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Consideration for purchase of redeemable noncontrolling interest in accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsRate_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tangible equity units, rate.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tangible Equity Units, Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tangible equity units, rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedObligationsUnderFinancingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Obligations under financing leases, net of current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedObligationsUnderFinancingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Obligations Under Financing Leases, Net Of Current Portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedObligationsUnderFinancingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Obligations Under Financing Leases, Net Of Current Portion.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrecognized share-based compensation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Assets, Fair Value Disclosure, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Fair Value Disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Financial assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SellingGeneralAndAdministrativeExpenseNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Selling, general and administrative expense not allocated at segment level.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SellingGeneralAndAdministrativeExpenseNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Selling General and Administrative Expense Not Allocated at Segment Level</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SellingGeneralAndAdministrativeExpenseNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Selling, general, and administrative expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk, Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">% of Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Revenues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Revenues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Revenues_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Revenues, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Revenues_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Products revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash provided by (used in) investing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDispositionOfRealEstateDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pre-tax gain on sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDispositionOfRealEstateDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) on Disposition of Real Estate, Discontinued Operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDispositionOfRealEstateDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gain on sale of discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operation, Gain (Loss) on Disposal of Discontinued Operation, Net of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Discontinued Operation, Gain (Loss) on Disposal of Discontinued Operation, Net of Tax, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Gain on sale of discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Gain on sale of discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ForwardStartingContractsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Forward starting contracts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ForwardStartingContractsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Forward Starting Contracts [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ForwardStartingContractsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Forward Starting Contracts [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_Security12bTitle_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Title of 12(b) Security</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_Security12bTitle_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title of 12(b) Security</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related and Nonrelated Parties [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RebateReceivableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Rebate receivable current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RebateReceivableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Rebate receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Accrued Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Payable [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trade Accounts Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentInformationTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Information [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Liabilities, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ConsolidatedEntitiesAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consolidated Entities [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Increase (Decrease) in Operating Capital [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Change in operating assets and liabilities, net of acquisitions and dispositions:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentPortionOfObligationsUnderOperatingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business combination recognized identifiable assets acquired and liabilities assumed current portion of obligations under operating leases.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentPortionOfObligationsUnderOperatingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Current Portion Of Obligations Under Operating Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentPortionOfObligationsUnderOperatingLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current portion of obligations under operating leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LettersOfCreditOutstandingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Letters of Credit Outstanding, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LettersOfCreditOutstandingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Letter of credit outstanding amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotesPayableAndOtherMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Notes payable and other.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotesPayableAndOtherMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Notes Payable and Other [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotesPayableAndOtherMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Notes Payable and Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfSharesUnderIncentiveAndShareBasedCompensationPlansIncludingStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Proceeds, Issuance of Shares, Share-Based Payment Arrangement, Including Option Exercised, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfSharesUnderIncentiveAndShareBasedCompensationPlansIncludingStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds, Issuance of Shares, Share-Based Payment Arrangement, Including Option Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfSharesUnderIncentiveAndShareBasedCompensationPlansIncludingStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from shares issued under share-based compensation plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Recurring and Nonrecurring [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CashFlowsFromDiscontinuedOperationsOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash flows from discontinued operations operating activities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CashFlowsFromDiscontinuedOperationsOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cash flows from discontinued operations operating activities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CashFlowsFromDiscontinuedOperationsOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash flows from operating activities of discontinued operations:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PercentageOfAggregateAnnualQuarterlyCashInstallmentsEquivalentPerYear_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of Aggregate Annual Quarterly Cash Installments Equivalent Per Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PercentageOfAggregateAnnualQuarterlyCashInstallmentsEquivalentPerYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage of Aggregate Annual Quarterly Cash Installments Equivalent Per Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_PercentageOfAggregateAnnualQuarterlyCashInstallmentsEquivalentPerYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of aggregate annual quarterly cash installments equivalent per year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementFrequencyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Measurement Frequency [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementLocationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Income Location, Balance [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_InterestExpenseNetExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest expense, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_InterestExpenseNetExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Expense, Net Expenses not Allocated at Segment Level</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_InterestExpenseNetExpensesNotAllocatedAtSegmentLevel_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Interest expense, net expenses not allocated at segment level.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Trading Symbol</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trading Symbol</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TwentyTwentyFourEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2024 Equity Incentive Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TwentyTwentyFourEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Twenty Twenty Four Equity Incentive Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TwentyTwentyFourEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">2024 Equity incentive plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationGainLossFromDisposalOfDiscontinuedOperationBeforeIncomeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operation, Gain (Loss) from Disposal of Discontinued Operation, before Income Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationGainLossFromDisposalOfDiscontinuedOperationBeforeIncomeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Gain on sale of discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationPrepaidAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Prepaid and Other Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationPrepaidAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), before Reclassification, Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income tax effects of net change in fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Employee-related Liabilities, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee-related Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Wages and payroll taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Financing activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsRecurringMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Recurring [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsRecurringMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Measurement Recurring</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncontrolling Interest Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable Noncontrolling Interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Components [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityComponentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Component [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TwoThousandTwentyFourAcquisitionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2024 Acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TwoThousandTwentyFourAcquisitionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty Four Acquisitions [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TwoThousandTwentyFourAcquisitionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand twenty four acquisitions member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill and Intangible Assets Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtInstrumentDelayedDraw_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt instrument, delayed draw.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtInstrumentDelayedDraw_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Delayed Draw</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtInstrumentDelayedDraw_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Delayed draw</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDeferredIncomeTaxesNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred income taxes, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDeferredIncomeTaxesNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Deferred Income Taxes Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDeferredIncomeTaxesNet_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business combination, recognized identifiable assets acquired and liabilities assumed, deferred income taxes net.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RepurchasesOfCommonStockInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Repurchases of common stock in accounts payable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RepurchasesOfCommonStockInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Repurchases Of Common Stock In Accounts Payable</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired and Liability Assumed [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Consideration Paid for Acquisitions and Estimated Fair Value of Assets Acquired and Liabilities Assumed</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidInsurance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Insurance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidInsurance_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid insurance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IPOMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">IPO [Member]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SecondLienCreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Second lien credit agreement member.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermNotesPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Notes Payable, Noncurrent</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermNotesPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term portion of the amortizing notes</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Depreciation and amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment depreciation and amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Comprehensive Income [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Maximum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Assets, Accumulated Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Definite-lived assets, Accumulated Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Value, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, $0.01 par value, 1,500,000,000 shares authorized, 193,209,722 and 192,124,125 shares issued and outstanding at March 31, 2026 and December 31, 2025, respectively</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeFixedInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative, Fixed Interest Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeFixedInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fixed rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeasePrincipalPayments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Principal Payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeasePrincipalPayments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Payment of financing lease obligations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeasePrincipalPayments_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Payments of financing lease obligations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConsolidationPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consolidation, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConsolidationPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Principles of Consolidation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationObligationsUnderFinancingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Obligations under Financing Leases, Net of Current Portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationObligationsUnderFinancingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal Group, Including Discontinued Operation, Obligations under Financing Leases, Net of Current Portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationObligationsUnderFinancingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Obligations under financing leases, net of current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationSellerNotePayable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business combination seller note payable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationSellerNotePayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Seller Note Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationSellerNotePayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Business combination seller note payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsPerDilutedShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Continuing operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsPerDilutedShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations, Per Diluted Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AmortizationOfFinancingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amortization of Debt Issuance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AmortizationOfFinancingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortization of deferred debt issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Carrying value as of the balance sheet date of long-term liabilities noncurrent (with maturities initially due after one year or beyond the operating cycle if longer), excluding current portion.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-term Liabilities Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total long-term liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LongTermLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ScheduleOfVolumeWeightedAveragePriceOfCommonStockTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule of volume weighted average price of common stock.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ScheduleOfVolumeWeightedAveragePriceOfCommonStockTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Volume Weighted Average Price of Common Stock [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ScheduleOfVolumeWeightedAveragePriceOfCommonStockTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Number of Common Stock Issued Based on 20 Day Volume Weighted-Average Price of Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RecognizingOfCostsRelatedToNewEquityAwardsGranted_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Recognizing of costs related to new equity awards granted.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RecognizingOfCostsRelatedToNewEquityAwardsGranted_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Recognizing of Costs Related to New Equity Awards Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_RecognizingOfCostsRelatedToNewEquityAwardsGranted_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Recognizing of costs related to new equity awards granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred Stock, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Comprehensive Income (Loss), Net of Tax, Attributable to Noncontrolling Interest, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income (Loss), Net of Tax, Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Comprehensive income (loss) attributable to noncontrolling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareDMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Medicare D.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareDMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Medicare D [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareDMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Medicare D</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MedicareDMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Medicare Part D</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Assets by Major Class [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SellingGeneralAndAdministrativeExpenseFromReportableSegment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment selling, general, and administrative expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SellingGeneralAndAdministrativeExpenseFromReportableSegment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Selling General and Administrative Expense From Reportable Segment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SellingGeneralAndAdministrativeExpenseFromReportableSegment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Selling general and administrative expense from reportable segment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Taxes paid related to net share settlement of equity awards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payment, Tax Withholding, Share-Based Payment Arrangement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_KkrCapitalMarketsLlcMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">KKR Capital Markets, LLC.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_KkrCapitalMarketsLlcMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">KKR Capital Markets, LLC [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_KkrCapitalMarketsLlcMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">KKR Capital Markets, LLC</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue from Contract with Customer [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CustomerConcentrationRiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Customer Concentration Risk [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CustomerConcentrationRiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Customer Concentration Risk</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConversionOfStockSharesIssued1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Conversion of Stock, Shares Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConversionOfStockSharesIssued1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConversionOfStockSharesIssued1_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Mandatory conversion to common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Events [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LitigationEstimatedSettlementAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Litigation estimated settlement amount.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LitigationEstimatedSettlementAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Litigation Estimated Settlement Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_LitigationEstimatedSettlementAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated settlement amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CovenantsNotToCompleteMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Covenants Not to Complete.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CovenantsNotToCompleteMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Covenants Not to Complete [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CovenantsNotToCompleteMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Covenants Not to Complete</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">SOFR</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationsHeldforsaleMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Discontinued operation held for sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationsHeldforsaleMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operations, Held-for-Sale [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ConsolidatedEntitiesDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consolidated Entities [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income Tax Expense (Benefit), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Expense (Benefit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Income tax benefit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income tax expense (benefit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Income tax benefit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByMeasurementFrequencyAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Measurement Frequency [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsStatedAmountPerUnit_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tangible equity units, stated amount per unit.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsStatedAmountPerUnit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tangible Equity Units, Stated Amount Per Unit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsStatedAmountPerUnit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tangible equity units, stated price per unit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationIncomeLossFromDiscontinuedOperationNetOfTaxPerBasicShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operation, Income (Loss) from Discontinued Operation, Net of Tax, Per Basic Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationIncomeLossFromDiscontinuedOperationNetOfTaxPerBasicShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SellersRestrictionTradingLockUpPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sellers restriction trading lock up period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SellersRestrictionTradingLockUpPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Sellers restriction trading lock up period.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SellersRestrictionTradingLockUpPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sellers Restriction Trading Lock Up Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdvancesOnInventoryPurchases_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Advances on Inventory Purchases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdvancesOnInventoryPurchases_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Inventory returns receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsidiary, Ownership Percentage, Noncontrolling Owner</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Ownership interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SecondLienPayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Second Lien - Payable To Lenders At Sofr Plus Applicable Margin [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SecondLienPayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Second Lien - Payable to Lenders at SOFR plus Applicable Margin</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SecondLienPayableToLendersAtSofrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Second lien - payable to lenders at SOFR plus applicable margin member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Common Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Common Stock, Shares Outstanding (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupClassificationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group Classification [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationSellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Selling, General and Administrative Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationSellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal Group, Including Discontinued Operation, Selling, General and Administrative Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DisposalGroupIncludingDiscontinuedOperationSellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Selling, general, and administrative expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accumulated Other Comprehensive Income (Loss), Net of Tax, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated other comprehensive loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ConsolidationItemsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consolidation Items [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedAutomobileInsuranceReservesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Carrying Value As Of The Balance Sheet Date Of Obligations Incurred And Payable For Accrued Automobile Insurance Reserves Current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedAutomobileInsuranceReservesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Automobile Insurance Reserves Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AccruedAutomobileInsuranceReservesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Automobile insurance reserves</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments and Contingencies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SharesWithheldRelatedToNetShareSettlementShares_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares withheld related to net share settlement, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SharesWithheldRelatedToNetShareSettlementShares_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares Withheld Related To Net Share Settlement, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SharesWithheldRelatedToNetShareSettlementShares_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Shares withheld related to net share settlement, shares.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NetLossExcludingAllocableRedeemableNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Net loss excluding allocable redeemable noncontrolling interests.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NetLossExcludingAllocableRedeemableNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Loss Excluding Allocable Redeemable Noncontrolling Interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NetLossExcludingAllocableRedeemableNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss excluding allocable redeemable noncontrolling interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Payments to Acquire Property, Plant, and Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchases of property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Purchases of property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForProceedsFromOtherInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payment for (Proceeds from) Other Investing Activity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForProceedsFromOtherInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForProceedsFromOtherInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CurrentAndDeferredTaxImpactOnRealEstateDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less: current and deferred tax impact</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CurrentAndDeferredTaxImpactOnRealEstateDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current and Deferred Tax Impact on Real Estate Discontinued Operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CurrentAndDeferredTaxImpactOnRealEstateDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Current and deferred tax impact on real estate discontinued operations.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Statement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EffectiveIncomeTaxRateReconciliationExpectedPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Expected Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EffectiveIncomeTaxRateReconciliationExpectedPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Effective income tax rate reconciliation, expected percent.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EffectiveIncomeTaxRateReconciliationExpectedPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated annual effective tax rate before discrete items</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Pro Forma Information [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Selling, general, and administrative expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Selling, General, and Administrative Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Selling, General and Administrative Expenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SwinglineBaseRatePayableToLendersAtAbrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Swingline/base Rate - Payable To Lenders At Abr Plus Applicable Margin [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SwinglineBaseRatePayableToLendersAtAbrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Swingline/Base Rate - Payable to Lenders at ABR plus Applicable Margin</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_SwinglineBaseRatePayableToLendersAtAbrPlusApplicableMarginMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Swingline/base rate - payable to lenders at ABR plus applicable margin member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityInitiationDate1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Initiation Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityInitiationDate1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Line of credit facility, agreement date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock on initial public offering, net, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CommercialInsuranceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Commercial Insurance.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CommercialInsuranceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commercial Insurance [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_CommercialInsuranceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commercial Insurance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDilutedAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Diluted [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDilutedAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Diluted income per share attributable to common shareholders:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Loss per share - diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net income (loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net income per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Segment Reporting Information, by Segment [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Segment Reporting Information</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingSegmentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Segments [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingSegmentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayableTrade_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accounts Payable, Trade</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayableTrade_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trade accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationTaxCreditsForeign_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income tax rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationTaxCreditsForeign_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Tax Credit, Foreign, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtDisclosureAndDerivativeFinancialInstrumentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Disclosure and Derivative Financial Instruments [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtDisclosureAndDerivativeFinancialInstrumentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt and Derivatives</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DebtDisclosureAndDerivativeFinancialInstrumentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt disclosure and derivative financial instruments.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total assets held for sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CityAreaCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">City Area Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CityAreaCode_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">City Area Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EarningsPerShareLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Earnings per share.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_EarningsPerShareLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings per Share [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionsProFormaRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Pro Forma Information, Pro Forma Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionsProFormaRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proforma revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionsProFormaRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Net of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other comprehensive income , net of tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total other comprehensive income (loss), net of tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProvisionForLoanLossesExpensed_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Credit Loss, Expense (Reversal)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProvisionForLoanLossesExpensed_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Provision for credit losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LicensingAgreementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Licensing Agreements [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LicensingAgreementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Licenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationTaxEffectOfDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operation, Tax Effect of Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationTaxEffectOfDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income tax expense of discontinued operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Obligations under financing leases, net of current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Face Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Principal amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net income (loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Discontinued Operations, Net of Tax, Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income from discontinued operations, net of income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfIntangibleAssetsAndGoodwillTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Intangible Assets and Goodwill [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfIntangibleAssetsAndGoodwillTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Intangible Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Gross borrowing</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Line of credit facility, maximum borrowing capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Business Acquisition [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherIntangibleAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Intangible Assets [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tangible equity units.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">TEUs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">6.75% Tangible Equity Unit [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_TangibleEquityUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Six Point Seven Five Percentage Tangible Equity Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RepurchaseAgreementCounterpartyNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Counterparty Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Amounts reclassified to earnings, net of tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), Reclassification, after Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingInformationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting Information [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stockholders' Equity Note, Stock Split, Conversion Ratio</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock split ratio</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock for settlement of RSUs, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, Restricted Stock Award, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group Name [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NumberOfBranchesToBeAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of branches to be acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NumberOfBranchesToBeAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number Of Branches To Be Acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NumberOfBranchesToBeAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of branches to be acquired.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateCashFlowHedgeLiabilityAtFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair value of interest rate swaps liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateCashFlowHedgeLiabilityAtFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Cash Flow Hedge Liability at Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ContingentConsiderationMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Contingent consideration.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ContingentConsiderationMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Contingent consideration [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ContingentConsiderationMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Contingent Consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DoctorPayorNetworkMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Doctor Payor Network.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DoctorPayorNetworkMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Doctor Payor Network [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_DoctorPayorNetworkMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Doctor/Payor Network</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LetterOfCreditMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Letter of Credit [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LetterOfCreditMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Letter of Credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share value calculated</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Consideration Transferred, Equity Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Property, Plant and Equipment, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment, net of accumulated depreciation of $421,329 and $404,878 at March 31, 2026 and December 31, 2025, respectively</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwillNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Goodwill, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwillNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Liabilities, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Disposal Group, Including Discontinued Operation, Liabilities, Noncurrent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-current liabilities held for sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash and cash equivalents included in continuing operations at end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Cash and cash equivalents at end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Cash and cash equivalents at beginning of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Income (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating income (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Operating income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillForeignCurrencyTranslationGainLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill, Foreign Currency Translation, Gain (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillForeignCurrencyTranslationGainLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign currency adjustments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotesIssuedInConnectionWithAcquisitions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Notes issued in connection with acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotesIssuedInConnectionWithAcquisitions_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Notes issued in connection with acquisitions.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NotesIssuedInConnectionWithAcquisitions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Notes issued in connection with acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NetProceedsFromTangibleEquityUnitsIssuance_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Net proceeds from tangible equity units issuance.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NetProceedsFromTangibleEquityUnitsIssuance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Proceeds from Tangible Equity Units Issuance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_NetProceedsFromTangibleEquityUnitsIssuance_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net proceeds from tangible equity units issuance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">(Accumulated Deficit) Retained Earnings</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AmortizingNotesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amortizing notes.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AmortizingNotesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amortizing Notes [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_AmortizingNotesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortizing Notes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other assets, noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Share-Based Payment Arrangement, Noncash Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Noncash Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureTextBlockSupplementAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disclosure Text Block Supplement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfFinancialPositionLocationActivityCapitalizationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Financial Position Location, Activity, Capitalization [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Obligations under operating leases, net of current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfStockLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net cash (used in) provided by financing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash used in financing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxLiabilitiesNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Income Tax Liabilities, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxLiabilitiesNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred income taxes, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedObligationsUnderOperatingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business combination recognized identifiable assets acquired and liabilities assumed obligations under operating leases, net of current portion.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedObligationsUnderOperatingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Obligations Under Operating Leases, Net Of Current Portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedObligationsUnderOperatingLeasesNetOfCurrentPortion_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Obligations under operating leases, net of current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepositsAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deposits Assets, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepositsAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deposits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MonitoringAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Monitoring agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MonitoringAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Monitoring Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_MonitoringAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Monitoring Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeContractTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Contract [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfGoodwillTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired, Receivable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts receivable</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityInteractiveDataCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Interactive Data Current</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_ServicingPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Servicing period.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="btsg_BasicEarningsLossPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Basic earnings loss per share.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfStockDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfStockByClassTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock, Class of Stock [Table]</link:label>
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  <xsd:element id="btsg_DeferredIncomeTaxesExpenseBenefit" name="DeferredIncomeTaxesExpenseBenefit" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
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  <xsd:element id="btsg_PrivateAndOtherMember" name="PrivateAndOtherMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
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  <xsd:element id="btsg_SHCMedicalPartnersLLCMember" name="SHCMedicalPartnersLLCMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_ForwardStartingContractsMember" name="ForwardStartingContractsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
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  <xsd:element id="btsg_AdjustmentOfRedeemableNoncontrollingInterestToRedemptionAmount" name="AdjustmentOfRedeemableNoncontrollingInterestToRedemptionAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
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  <xsd:element id="btsg_OtherPrepaidExpensesAndCurrentAssets" name="OtherPrepaidExpensesAndCurrentAssets" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
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  <xsd:element id="btsg_IndefiniteLivedLicensesMember" name="IndefiniteLivedLicensesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_AccruedLiabilitiesCurrentMember" name="AccruedLiabilitiesCurrentMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
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  <xsd:element id="btsg_StockRepurchasedDuringPeriodValues" name="StockRepurchasedDuringPeriodValues" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_TaxEffectOfNetShareSettlementOfEquityAwards" name="TaxEffectOfNetShareSettlementOfEquityAwards" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_GatewayPediatricTherapyLlcMember" name="GatewayPediatricTherapyLlcMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
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  <xsd:element id="btsg_SeniorAmortizingNoteMember" name="SeniorAmortizingNoteMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
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  <xsd:element id="btsg_SharesWithheldRelatedToNetShareSettlementValue" name="SharesWithheldRelatedToNetShareSettlementValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_ExistingContractsInterestRateSwapAgreementsMember" name="ExistingContractsInterestRateSwapAgreementsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_CarryingAmountOfCommunityLivingBusiness" name="CarryingAmountOfCommunityLivingBusiness" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_SummaryOfSignificantAccountingPolicyTable" name="SummaryOfSignificantAccountingPolicyTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_AccruedAutomobileInsuranceReservesCurrent" name="AccruedAutomobileInsuranceReservesCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_MizuhoCapitalMarketsMember" name="MizuhoCapitalMarketsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_ComprehensiveIncomeLossNetOfTaxAttributableToRedeemableNoncontrollingInterest" name="ComprehensiveIncomeLossNetOfTaxAttributableToRedeemableNoncontrollingInterest" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_PercentageOfEbitdaPayableAsAdvisoryFee" name="PercentageOfEbitdaPayableAsAdvisoryFee" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="btsg_LcFacilityMember" name="LcFacilityMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_RevolvingCreditLoansPayableToLendersAtSofrPlusApplicableMarginMember" name="RevolvingCreditLoansPayableToLendersAtSofrPlusApplicableMarginMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_TwentySeventeenStockPlanMember" name="TwentySeventeenStockPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_TangibleEquityUnitsPurchaseContractsMember" name="TangibleEquityUnitsPurchaseContractsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_HavenHospiceIncMember" name="HavenHospiceIncMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_IssuanceOfDebtAndCommonStockPricePerShare" name="IssuanceOfDebtAndCommonStockPricePerShare" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="btsg_TrancheB5TermLoanMember" name="TrancheB5TermLoanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_ExpensesNotAllocatedAtSegmentLevelAbstract" name="ExpensesNotAllocatedAtSegmentLevelAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_TerminationFeesPaid" name="TerminationFeesPaid" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_NotesIssuedInConnectionWithAcquisitions" name="NotesIssuedInConnectionWithAcquisitions" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_CommonStockSharesPurchased" name="CommonStockSharesPurchased" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_SecondLienCreditAgreementMember" name="SecondLienCreditAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_SellersRestrictionTradingLockUpPeriod" name="SellersRestrictionTradingLockUpPeriod" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_ProfitLossExcludingRedeemableNoncontrollingInterests" name="ProfitLossExcludingRedeemableNoncontrollingInterests" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_OtherMember" name="OtherMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_ScheduleOfIntangibleAssetsLineItems" name="ScheduleOfIntangibleAssetsLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_DebtInstrumentDelayedDraw" name="DebtInstrumentDelayedDraw" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_NetLossExcludingAllocableRedeemableNoncontrollingInterests" name="NetLossExcludingAllocableRedeemableNoncontrollingInterests" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_ScheduleOfProceedsFromIssuanceOfTangibleEquityUnitsAllocatedToEquityAndDebtTableTextBlock" name="ScheduleOfProceedsFromIssuanceOfTangibleEquityUnitsAllocatedToEquityAndDebtTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_SummaryOfSignificantAccountingPolicyLineItems" name="SummaryOfSignificantAccountingPolicyLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_AccruedLegalSettlementsAndProfessionalFeesCurrent" name="AccruedLegalSettlementsAndProfessionalFeesCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_DisposalGroupIncludingDiscontinuedOperationCurrentPortionOfObligationsUnderFinancingLeases" name="DisposalGroupIncludingDiscontinuedOperationCurrentPortionOfObligationsUnderFinancingLeases" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_DebtFinancingFeesPaid" name="DebtFinancingFeesPaid" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_EffectiveIncomeTaxRateReconciliationExpectedPercent" name="EffectiveIncomeTaxRateReconciliationExpectedPercent" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_DistributionOfFundCovid19" name="DistributionOfFundCovid19" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_DebtDisclosureAndDerivativeFinancialInstrumentsTextBlock" name="DebtDisclosureAndDerivativeFinancialInstrumentsTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_KohlbergKravisRobertsCoLPAndWalgreensBootsAllianceIncMember" name="KohlbergKravisRobertsCoLPAndWalgreensBootsAllianceIncMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_FinancingLeaseObligations" name="FinancingLeaseObligations" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_SellingGeneralAndAdministrativeExpenseFromReportableSegment" name="SellingGeneralAndAdministrativeExpenseFromReportableSegment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_CertainPostClosingAdjustments" name="CertainPostClosingAdjustments" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_ScheduleOfVolumeWeightedAveragePriceOfCommonStockTableTextBlock" name="ScheduleOfVolumeWeightedAveragePriceOfCommonStockTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_NumberOfCustomer" name="NumberOfCustomer" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_AmedisysAndLHCBranchesAcquisitionMember" name="AmedisysAndLHCBranchesAcquisitionMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_LessThanThirteenPointZeroZeroMember" name="LessThanThirteenPointZeroZeroMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_CovenantsNotToCompleteMember" name="CovenantsNotToCompleteMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_AccruedPropertyInsuranceReserves" name="AccruedPropertyInsuranceReserves" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_DisposalGroupIncludingDiscontinuedOperationObligationsUnderOperatingLeasesNetOfCurrentPortion" name="DisposalGroupIncludingDiscontinuedOperationObligationsUnderOperatingLeasesNetOfCurrentPortion" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_DisposalGroupIncludingDiscontinuedOperationSellingGeneralAndAdministrativeExpense" name="DisposalGroupIncludingDiscontinuedOperationSellingGeneralAndAdministrativeExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_TangibleEquityUnitsIssuedDuringPeriodNewIssues" name="TangibleEquityUnitsIssuedDuringPeriodNewIssues" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_StockRepurchasedDuringPeriodShare" name="StockRepurchasedDuringPeriodShare" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_PaymentOfUnderwritingDiscountsAndCommissions" name="PaymentOfUnderwritingDiscountsAndCommissions" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_CurrentAndDeferredTaxImpactOnRealEstateDiscontinuedOperations" name="CurrentAndDeferredTaxImpactOnRealEstateDiscontinuedOperations" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_MedicaidMember" name="MedicaidMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_SwinglineLoansMember" name="SwinglineLoansMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_AlternateBaseRateMember" name="AlternateBaseRateMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_ContingentConsiderationMember" name="ContingentConsiderationMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_BusinessCombinationSellerNotePayable" name="BusinessCombinationSellerNotePayable" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_BusinessAcquisitionCostOfAcquiredEntityTransactionCosts1" name="BusinessAcquisitionCostOfAcquiredEntityTransactionCosts1" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_RecognizingOfCostsRelatedToNewEquityAwardsGranted" name="RecognizingOfCostsRelatedToNewEquityAwardsGranted" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_FirstLienIncrementalTermLoanTrancheB5PayableToLendersAtSofrPlusApplicableMarginMember" name="FirstLienIncrementalTermLoanTrancheB5PayableToLendersAtSofrPlusApplicableMarginMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_LongTermLiabilitiesInterestRateSwaps" name="LongTermLiabilitiesInterestRateSwaps" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_TrancheB3TermLoanMember" name="TrancheB3TermLoanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_CashFlowsFromDiscontinuedOperationsOperatingActivitiesAbstract" name="CashFlowsFromDiscontinuedOperationsOperatingActivitiesAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_TangibleEquityUnitsRate" name="TangibleEquityUnitsRate" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="btsg_DoctorPayorNetworkMember" name="DoctorPayorNetworkMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_NotesReceivableNoncurrent" name="NotesReceivableNoncurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_TwentyTwentyFourEquityIncentivePlanMember" name="TwentyTwentyFourEquityIncentivePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncontrollingInterests" name="BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncontrollingInterests" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_NumberOfBranchesToBeAcquired" name="NumberOfBranchesToBeAcquired" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_ConversionOfTangibleEquityUnitsIntoCommonStockShare" name="ConversionOfTangibleEquityUnitsIntoCommonStockShare" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_UnderwriterArrangerAndTransactionFees" name="UnderwriterArrangerAndTransactionFees" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_ProviderServicesMember" name="ProviderServicesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_BasicEarningsLossPerShareAbstract" name="BasicEarningsLossPerShareAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_LcSublimitMember" name="LcSublimitMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_CommunityLivingBusinessMember" name="CommunityLivingBusinessMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_ServicingPeriod" name="ServicingPeriod" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_DuesAndSubscriptions" name="DuesAndSubscriptions" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_LitigationEstimatedSettlementAmount" name="LitigationEstimatedSettlementAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_PrepaidInterestRateSwaps" name="PrepaidInterestRateSwaps" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRedeemableNoncontrollingInterests" name="BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRedeemableNoncontrollingInterests" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_LossOnExtinguishmentOfDebtExpensesNotAllocatedAtSegmentLevel" name="LossOnExtinguishmentOfDebtExpensesNotAllocatedAtSegmentLevel" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_DepreciationAndAmortizationExpensesNotAllocatedAtSegmentLevel" name="DepreciationAndAmortizationExpensesNotAllocatedAtSegmentLevel" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_LongTermLiabilitiesAutomobileInsuranceReservesNoncurrent" name="LongTermLiabilitiesAutomobileInsuranceReservesNoncurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_ThresholdAmountToDetermineCommonStockIssuance" name="ThresholdAmountToDetermineCommonStockIssuance" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_DebtInstrumentConvertibleCashInstallmentPerUnit" name="DebtInstrumentConvertibleCashInstallmentPerUnit" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="btsg_FirstLienPayableToLendersAtSofrPlusApplicableMarginMember" name="FirstLienPayableToLendersAtSofrPlusApplicableMarginMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_PrepaidMaintenance" name="PrepaidMaintenance" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_RelatedPartyTransactionsPolicyTextBlock" name="RelatedPartyTransactionsPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_AccruedChecksInExcessOfCashBalanceCurrent" name="AccruedChecksInExcessOfCashBalanceCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_BusinessAcquisitionNumberOfBranches" name="BusinessAcquisitionNumberOfBranches" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_CommonStockPreferredStockAndShareBasedCompensationTextBlock" name="CommonStockPreferredStockAndShareBasedCompensationTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_CostOfServices" name="CostOfServices" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_DisposalGroupIncludingDiscontinuedOperationObligationsUnderFinancingLeasesNetOfCurrentPortion" name="DisposalGroupIncludingDiscontinuedOperationObligationsUnderFinancingLeasesNetOfCurrentPortion" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_DebtInstrumentFloorRate" name="DebtInstrumentFloorRate" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_AccruedGeneralAndProfessionalLiabilityInsuranceReservesCurrent" name="AccruedGeneralAndProfessionalLiabilityInsuranceReservesCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_TwoThousandTwentyFiveAcquisitionMember" name="TwoThousandTwentyFiveAcquisitionMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_DisposalGroupIncludingDiscontinuedOperationAccumulatedDepreciationOfPropertyPlantAndEquipment" name="DisposalGroupIncludingDiscontinuedOperationAccumulatedDepreciationOfPropertyPlantAndEquipment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_LongTermLiabilitiesNoncurrentMember" name="LongTermLiabilitiesNoncurrentMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_HarvestGroveLTCLLCMember" name="HarvestGroveLTCLLCMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_OtherAssetsGross" name="OtherAssetsGross" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_TerminationFees" name="TerminationFees" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_PercentageOfAggregateAnnualQuarterlyCashInstallmentsEquivalentPerYear" name="PercentageOfAggregateAnnualQuarterlyCashInstallmentsEquivalentPerYear" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_MarchTwoThousandTwentySixOfferingMember" name="MarchTwoThousandTwentySixOfferingMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpenses" name="BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpenses" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentPortionOfObligationsUnderFinancingLeases" name="BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentPortionOfObligationsUnderFinancingLeases" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_TaxEffectOfNetShareSettlementOfEquityAwardsValue" name="TaxEffectOfNetShareSettlementOfEquityAwardsValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_TangibleEquityUnitsAmortizingNotesMember" name="TangibleEquityUnitsAmortizingNotesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_EarningsPerShareTable" name="EarningsPerShareTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_PaymentsForUnderwritingDiscountsAndCommissions" name="PaymentsForUnderwritingDiscountsAndCommissions" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_MorganStanleyMember" name="MorganStanleyMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_CashFlowsFromDiscontinuedOperationsInvestingActivitiesAbstract" name="CashFlowsFromDiscontinuedOperationsInvestingActivitiesAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_MedicareBMember" name="MedicareBMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_PharmacySolutionsAndProviderServicesMember" name="PharmacySolutionsAndProviderServicesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_ChangeInFairValueOfContingentConsiderationsNet" name="ChangeInFairValueOfContingentConsiderationsNet" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_LongTermLiabilitiesNoncurrent" name="LongTermLiabilitiesNoncurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_RebateReceivableCurrent" name="RebateReceivableCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_SharesWithheldRelatedToNetShareSettlementShares" name="SharesWithheldRelatedToNetShareSettlementShares" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_DepreciationAndAmortizationExpenseFromReportableSegment" name="DepreciationAndAmortizationExpenseFromReportableSegment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_CloudComputing" name="CloudComputing" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_RepurchasesOfCommonStockInAccountsPayable" name="RepurchasesOfCommonStockInAccountsPayable" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDeferredIncomeTaxesNet" name="BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDeferredIncomeTaxesNet" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_NotionalAmountToHedgeCashFlowRiskOfVariability" name="NotionalAmountToHedgeCashFlowRiskOfVariability" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_OctoberTwoThousandTwentyFiveOfferingMember" name="OctoberTwoThousandTwentyFiveOfferingMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_ServiceFees" name="ServiceFees" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_TradeReceivablesMember" name="TradeReceivablesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_AccrualForInterestRateSwapsCurrent" name="AccrualForInterestRateSwapsCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_MonitoringAndAdvisoryFees" name="MonitoringAndAdvisoryFees" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_RedemptionOfNoncontrollingInterestPercentage" name="RedemptionOfNoncontrollingInterestPercentage" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_TwoThousandTwentySixAcquisitionMember" name="TwoThousandTwentySixAcquisitionMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_DisposalGroupIncludingDiscontinuedOperationOperatingLeaseRight-Of-UseAssetsNet" name="DisposalGroupIncludingDiscontinuedOperationOperatingLeaseRight-Of-UseAssetsNet" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_DefiniteLivedLicensesMember" name="DefiniteLivedLicensesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_CostOfDrugs" name="CostOfDrugs" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_WeightedAveragePricePerPurchaseContract" name="WeightedAveragePricePerPurchaseContract" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOperatingLeaseRightOfUseAssets" name="BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOperatingLeaseRightOfUseAssets" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="btsg_GainLossOnDispositionOfRealEstateDiscontinuedOperationsNet" name="GainLossOnDispositionOfRealEstateDiscontinuedOperationsNet" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="btsg_FirstLienCreditAgreementMember" name="FirstLienCreditAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_TrancheB2TermLoanMember" name="TrancheB2TermLoanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_PharmacySolutionsAndProviderServicesSegmentsMember" name="PharmacySolutionsAndProviderServicesSegmentsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="btsg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedObligationsUnderFinancingLeasesNetOfCurrentPortion" name="BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedObligationsUnderFinancingLeasesNetOfCurrentPortion" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
</xsd:schema>
