Inclusion Criteria:

          -  Are participants with histologically or cytologically confirmed locally advanced or
             metastatic BTC

          -  Participants must have available tumor tissue (primary or metastatic) (archival or
             fresh biopsies) before the first administration of study treatment

          -  At least 1 measurable lesion according to RECIST 1.1

          -  Eastern Cooperative Oncology Group Performance Status (ECOG PS) of 0 or 1 at study
             entry and at Week 1, Day 1 prior to dosing

          -  Life expectancy of >= 12 weeks, as judged by the Investigator

          -  Adequate hematological function, hepatic function, renal function, coagulation
             function as defined in the protocol

          -  Hepatitis B virus (HBV) deoxyribonucleic acid (DNA) positive participants must be
             treated and on a stable dose of antivirals

          -  Other protocol defined inclusion criteria could apply

        Exclusion Criteria:

          -  Previous and/or intercurrent cancers

          -  Receipt of any organ transplantation, including allogeneic stem-cell transplantation,
             but with the exception of transplants that do not require immunosuppression

          -  Participants with symptomatic central nervous system (CNS) metastases

          -  Significant acute or chronic infection including known history of positive test for
             human immunodeficiency virus (HIV), active tuberculosis, uncontrolled biliary
             infection and active bacterial or fungal infection requiring systemic therapy (with
             the exception of hepatitis B and hepatitis C) requiring systemic therapy at study
             entry and at Week 1 Day 1 prior to dosing.

          -  Active autoimmune disease that might deteriorate when receiving an immunostimulatory
             agent

          -  History of or concurrent interstitial lung disease

          -  History of hypersensitivity reactions to bintrafusp alfa, anaphylaxis, or recent
             (within 5 months) uncontrolled asthma, cardiovascular/cerebrovascular disease

          -  Chronic obstructive pulmonary disease exacerbation or other respiratory illness
             requiring hospitalization or precluding study therapy within 30 days before
             randomization

          -  Prior therapy with any antibody/drug targeting T-cell coregulatory proteins (immune
             checkpoints)

          -  Other protocol defined exclusion criteria could apply