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<!-- DFIN ActiveDisclosure(SM) XBRL Schema Document - http://www.dfinsolutions.com/ -->
<!-- Creation Date      : 2021-05-10T18:26:32.4779399+00:00 -->
<!-- Version            : 5.0.1.615 -->
<!-- Package ID         : 440bbbaff6d24086ac5568b2d014b853 -->
<!-- Copyright (c) 2021 Donnelley Financial Solutions, Inc. All Rights Reserved. -->
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  <xsd:element id="bdsx_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsOutstandingWeightedAverageExercisePrice" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsOutstandingWeightedAverageExercisePrice" type="num:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xsd:element id="bdsx_ShareBasedCompensationArrangementsByShareBasedPaymentAwardNonOptionsGrantsInPeriodWeightedAverageExercisePrice" name="ShareBasedCompensationArrangementsByShareBasedPaymentAwardNonOptionsGrantsInPeriodWeightedAverageExercisePrice" type="num:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="bdsx_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsForfeituresAndExpirationsInPeriodWeightedAverageExercisePrice" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsForfeituresAndExpirationsInPeriodWeightedAverageExercisePrice" type="num:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="bdsx_ShareBasedCompensationArrangementsByShareBasedPaymentAwardNonOptionsExercisesInPeriodWeightedAverageExercisePrice" name="ShareBasedCompensationArrangementsByShareBasedPaymentAwardNonOptionsExercisesInPeriodWeightedAverageExercisePrice" type="num:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="bdsx_DiagnosticTestsMember" name="DiagnosticTestsMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="bdsx_AdvanceDeposits" name="AdvanceDeposits" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="bdsx_MedicareMember" name="MedicareMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="bdsx_TheBigTenConferenceMember" name="TheBigTenConferenceMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="bdsx_PfizerIncMember" name="PfizerIncMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="bdsx_CenturaHealthcareMember" name="CenturaHealthcareMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="bdsx_PurdueUniversityMember" name="PurdueUniversityMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="bdsx_TwoThousandTwentyEquityIncentivePlanMember" name="TwoThousandTwentyEquityIncentivePlanMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="bdsx_OptionsAndRestrictedStockUnitsRSUsMember" name="OptionsAndRestrictedStockUnitsRSUsMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="bdsx_BonusToOptionsProgramMember" name="BonusToOptionsProgramMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="bdsx_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsGrantedWeightedAverageRemainingContractualTerm1" name="SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsGrantedWeightedAverageRemainingContractualTerm1" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="bdsx_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantedAggregateIntrinsicValue" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantedAggregateIntrinsicValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="bdsx_OptionsToPurchaseCommonStockMember" name="OptionsToPurchaseCommonStockMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="bdsx_BDX004Member" name="BDX004Member" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="bdsx_FiclatuzumabMember" name="FiclatuzumabMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="bdsx_NSCLCPOCTrialMember" name="NSCLCPOCTrialMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="bdsx_POCClinicalTrialsMember" name="POCClinicalTrialsMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="bdsx_BioRadLicenseMember" name="BioRadLicenseMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="bdsx_RevenueShareAgreementMember" name="RevenueShareAgreementMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="bdsx_OncimmuneLimitedMember" name="OncimmuneLimitedMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="bdsx_PercentageOfDevelopmentAndRegulatoryCosts" name="PercentageOfDevelopmentAndRegulatoryCosts" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xsd:element id="bdsx_RemainingEstimatedObligation" name="RemainingEstimatedObligation" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="bdsx_PercentageOfRoyaltyPaymentsOnNetSales" name="PercentageOfRoyaltyPaymentsOnNetSales" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="bdsx_PercentageOfLicenseIncomeGeneratedFromLicensing" name="PercentageOfLicenseIncomeGeneratedFromLicensing" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="bdsx_PercentageOfRoyaltyPaymentsOnNetRevenue" name="PercentageOfRoyaltyPaymentsOnNetRevenue" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="bdsx_LicenseAgreementExpiryDate" name="LicenseAgreementExpiryDate" type="xbrli:gYearMonthItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="bdsx_PercentageOfRevenueSharePaymentRelatedToAcquiredDiagnosticTestRecognizedRevenueForNonScreeningTests" name="PercentageOfRevenueSharePaymentRelatedToAcquiredDiagnosticTestRecognizedRevenueForNonScreeningTests" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="bdsx_MinimumAnnualVolumePercentageThereafter" name="MinimumAnnualVolumePercentageThereafter" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="bdsx_PeriodOfEscalationsOfSales" name="PeriodOfEscalationsOfSales" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="bdsx_RevenueShareExpenses" name="RevenueShareExpenses" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
</xsd:schema>
