Inclusion Criteria:  Signed informed consent form Age ≥ 18 years by the time of inclusion in the study Ability to comply with the study protocol, in the investigator's judgment Histologically confirmed advanced BTC Patient must have received at least one prior line of systemic therapy in advanced-stage BTC Adjuvant or neoadjuvant chemotherapy is allowed, provided it is completed at least 6 months before start of study treatment Eastern Cooperative Oncology Group Performance Status (ECOG PS) of 0 or 1 Life expectancy > 12 weeks Measurable disease, according to RECIST v1.1. Lesions intended to be biopsied should not be defined as target lesions Tumor must be accessible for biopsies and patient willing to provide tissue from a newly obtained biopsy of a tumor lesion Adequate hematologic and end-organ function, defined by the following laboratory test results, obtained within 14 days prior to initiation of study treatment. For women of childbearing potential: Negative serum pregnancy test within 21 days prior to Cycle 1 Day 1 (C1D1). Agreement to remain abstinent (refrain from heterosexual intercourse) or use of contraceptive methods that result in a failure rate of ≤ 1% per year during the treatment period and for at least 180 days after the last study treatment For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive measures and agreement to refrain from donating sperm.  Exclusion Criteria:  Malignancies other than BTC within 3 years prior to C1D1 with the exception of those with a negligible risk of metastasis or death (e.g., expected 5-year overall survival > 90%) treated with expected curative outcome (such as adequately treated carcinoma in situ of the cervix, basal or squamous cell skin cancer, localized prostate cancer treated surgically, ductal carcinoma in situ treated surgically) Patients with known microsatellite instability high (MSI-H) status. Patients with unknown MSI status are eligible and the MSI status will be analyzed retrospectively. Patients who are then determined to be MSI-H will be allowed to continue the study treatment, but will be replaced by microsatellite-stable (MSS) or MSI-low tumors. Untreated central nervous system (CNS) metastases. Treatment of brain metastases, either by surgical or radiation techniques must have been completed at least 4 weeks prior to initiation of study treatment. Radiation therapy within 21 days prior to C1D1 and/or persistence of radiation-related adverse effects Prior allogeneic bone marrow transplantation or solid organ transplant for another malignancy in the past Spinal cord compression not definitively treated with surgery and/or radiation Uncontrolled pleural effusion, pericardial effusion, or ascites requiring recurrent drainage procedures Uncontrolled tumor pain. Patients who require narcotic pain medication during screening should be on a stable dose regimen prior to C1D1. Asymptomatic metastatic lesions that would likely cause functional deficits or intractable pain with further growth (e.g., epidural metastasis that is not currently associated with spinal cord compression) should be considered for loco-regional therapy if appropriate prior to enrollment. Treatment with any investigational agent or approved therapy within 28 days or two investigational agent half-lives (whichever is longer) prior to C1D1 Prior treatment with CD137 agonists or immune checkpoint blockade therapies, including anti-PD-1 and anti-PD-L1, or VEGF/VEGFR inhibitors Known dihydropyrimidine dehydrogenase deficiency or thymidylate synthase gene polymorphism predisposing the patient for 5-fluorouracil (5-FU) toxicity History of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins Known hypersensitivity or allergy to biopharmaceuticals produced in Chinese hamster ovary cells or any components of atezolizumab or bevacizumab formulations Current or recent (within 10 days of study enrollment) use of acetylsalicylic acid (> 325 mg/day), clopidogrel (> 75 mg/day) or thrombolytic agents for therapeutic purposes  History of clinically significant cardiac or pulmonary dysfunction including the following:  Inadequately controlled hypertension (that is defined as systolic blood pressure > 140 mmHg and/or diastolic blood pressure > 90 mmHg that is treated or untreated) Prior history of hypertensive crisis or hypertensive encephalopathy Significant vascular disease (e.g., aortic aneurysm requiring surgical repair or recent arterial thrombosis) within 6 months of C1D1 History of stroke or transient ischemic attack within 6 months prior to C1D1 Significant cardiovascular disease [such as New York Heart Association (NYHA) cardiac disease (Class II or greater), myocardial infarction, or cerebrovascular accident] within 3 months prior to C1D1, severe cardiac arrhythmia requiring medication or severe conduction abnormalities, unstable arrhythmias, acute coronary syndromes (including unstable angina), or history of coronary angioplasty/ stenting/bypass grafting within past 6 months. Patients with known left ventricular ejection fraction (LVEF) < 40% will be excluded Patients with known coronary artery disease, congestive heart failure not meeting the above criteria, or LVEF < 50% must be on a stable medical regimen that is optimized in the opinion of the treating physician, in consultation with a cardiologist if appropriate History of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans), drug-induced pneumonitis, idiopathic pneumonitis, or evidence of active pneumonitis on screening chest computed tomography (CT) scan Major surgical procedure within 4 weeks prior to C1D1 or anticipation of need for a major surgical procedure during the course of the study Evidence of tumor invading or abutting major blood vessels Serious non-healing wound, active ulcer or untreated bone fracture History of abdominal fistula or gastrointestinal perforation within 6 months prior to C1D1 History of hemoptysis (≥ ½ teaspoon of bright red blood per episode), or any other serious hemorrhage, or at risk of bleeding (gastrointestinal history of bleeds, gastrointestinal ulcers, etc.) INR > 1.5 and aPTT > 1.5 x ULN within 7 days prior to C1D1 (excluding patients on prophylactic or therapeutic anticoagulation) History or evidence of inherited bleeding diathesis or significant coagulopathy at risk of bleeding Proteinuria at screening as demonstrated by urine dipstick ≥ 2+ or 24-hour proteinuria > 1.0 g Treatment with systemic immunosuppressive medication (including, but not limited to, corticosteroids, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor (TNF)-alpha agents) within 2 weeks prior to initiation of study treatment, or anticipation of need for systemic immunosuppressive medication during study treatment Systemic immunostimulatory agents (including, but not limited to interferons and interleukin [IL]-2) are prohibited within 4 weeks or five half-lives of the drug (whichever is longer) prior to C1D1  Autoimmune conditions: History of autoimmune disease including but not limited to myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjögren's syndrome, Guillain-Barre syndrome, multiple sclerosis, vasculitis, or glomerulonephritis with the following exceptions:  Patients with a history of autoimmune-related hypothyroidism who are on thyroid replacement hormone are eligible for the study Patients with controlled Type 1 diabetes mellitus Patients with eczema, psoriasis, lichen simplex chronicus, or vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis are excluded) are eligible for the study provided all of following conditions are met: Rash must cover less than 10% of body surface area, disease is well controlled at baseline and requires only low-potency topical corticosteroids, no occurrence of acute exacerbations of the underlying condition requiring psoralen plus ultraviolet A radiation, methotrexate, retinoids, biologic agents, oral calcineurin inhibitors, or high potency or oral corticosteroids within the previous 12 months  Infectious diseases  Severe infection within 4 weeks prior to initiation of C1D1, including, but not limited to, hospitalization for complications of infection, bacteremia, or severe pneumonia Treatment with therapeutic oral or intravenous antibiotics within 2 weeks prior to initiation of study treatment Patients with active hepatitis B (chronic or acute; defined as having a positive hepatitis B surface antigen [HBsAg] test at screening) Patients with past hepatitis B virus (HBV) infection or resolved HBV infection (defined as the presence of hepatitis B core antibody [anti-HBc] and absence of HBsAg) are eligible. HBV DNA test must be performed in these patients prior to C1D1. Patients with active hepatitis C. Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV RNA. Positive HIV test at screening or at any time prior to screening. Patients without a prior positive HIV test result will undergo an HIV test at screening, unless not permitted per local regulations Known active tuberculosis Patients must not receive any kind of living, attenuated vaccine (e.g. Fluenz® Tetra) within 4 weeks prior to C1D1 or at any time during the study and for at least 5 months after the last dose of study drug. Pregnant or lactating or intending to become pregnant during the study or within 5 months after final dose for atezolizumab or 6 months for bevacizumab. Women who are not post-menopausal (≥ 12 continuous months of amenorrhea with no identified cause other than menopause) or surgically sterile must have a negative serum pregnancy test within 21 days prior to C1D1. Uncontrolled serious medical or psychiatric illness