Bevacizumab, Capecitabine, and Oxaliplatin in Treating Advanced Small Intestinal or Ampulla of Vater Adenocarcinoma

Inclusion Criteria: * Patients must have histologically confirmed adenocarcinoma of the small bowel or ampulla of Vater * Prior adjuvant chemotherapy (including fluorouracil \[5-FU\], capecitabine, and oxaliplatin) for the treatment of adenocarcinoma of the small bowel or ampulla of Vater is allowed if completed \>= 52 weeks prior to first dose of study treatment * Prior capecitabine or 5-FU administered as a radio-sensitizing agent concurrently with external beam radiotherapy is allowed * Patients must have metastatic disease * A minimum of 4 weeks must have elapsed from completion of any prior chemotherapy or radiotherapy or surgery and the start date of study therapy * Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2 * Absolute neutrophil count (ANC) \>= 1,500/ul * Platelets \>= 100,000/ul * Total bilirubin =\< 1.5 x upper limit of normal (ULN) * In patients with known Gilbert's syndrome direct bilirubin =\< 1.5 x ULN will be used as organ function criteria, instead of total bilirubin * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) \< 3 x ULN * Calculated creatinine clearance (CrCl) \> 50 cc/min (calculated using the Cockcroft and Gault formula) * Negative serum or urine pregnancy test in women with childbearing potential (defined as not post-menopausal for 12 months or no previous surgical sterilization), within one week prior to initiation of treatment * Patients must sign an Informed Consent and Authorization indicating that they are aware of the investigational nature of this study and the known risks involved * The effects of the combination of CAPOX and bevacizumab on the developing fetus are unknown. For this reason, women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control) prior to study entry, for the duration of study participation, and for six months following the completion of therapy. Should a woman become pregnant while participating in this study, she should inform her treating physician immediately * Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with oxaliplatin or capecitabine or bevacizumab, breast feeding must be discontinued Exclusion Criteria: * Patients who have received prior chemotherapy for their metastatic disease are excluded. Chemotherapy if given as a radiation-sensitizer is allowed * Patients may not be receiving any other investigational agents nor have received any investigational drug 28 days prior to enrollment * Known history of dihydropyrimidine (DPD) deficiency * Peripheral neuropathy of grade 3 or greater by Common Terminology Criteria for Adverse Events (CTCAE) 4.0 * Gastrointestinal tract disease resulting in an inability to take oral medication or a requirement for IV alimentation * Because of the interaction between coumadin and capecitabine, patients taking therapeutic doses of coumadin-derivative anticoagulants are not eligible. Low-dose coumadin (e.g. 1 mg PO per day) in patients with in-dwelling venous access devices is allowed but increased frequency of international normalized ratio (INR) monitoring is recommended * Prior treatment with bevacizumab or known hypersensitivity to any component of bevacizumab * Inadequately controlled hypertension (defined as systolic blood pressure \>140 mmHg and/or diastolic blood pressure \> 90 mmHg) * Prior history of hypertensive crisis or hypertensive encephalopathy * Evidence of bleeding diathesis or significant coagulopathy (in the absence of therapeutic anticoagulation) * New York Heart Association (NYHA) grade II or greater congestive heart failure * History of myocardial infarction or unstable angina within 6 months prior to day 1 * History of stroke or transient ischemic attack within 6 months prior to day 1. * Significant vascular disease (e.g., aortic aneurysm, requiring surgical repair or recent peripheral arterial thrombosis) within 6 months prior to day 1 * History of hemoptysis (\>= 1/2 teaspoon of bright red blood per episode) within 1 month prior to day 1 * History of abdominal fistula or gastrointestinal perforation which must have resolved at least 6 months prior to day 1 * Major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to day 1 or anticipation of need for major surgical procedure during the course of the study * Core biopsy or other minor surgical procedure excluding placement of a vascular access device, within 7 days prior to day 1 * Serious, non-healing wound, active ulcer, or untreated bone fracture * Proteinuria at screening as demonstrated by either (1) urine protein:creatinine (UPC) ratio of \>= 1.0 or (2) urine dipstick for proteinuria \>= 2+ (patients discovered to have \>/= 2+ proteinuria on dipstick urinalysis should undergo a 24 hour urine collection and must demonstrate =\< 1g of protein in 24 hours to be eligible) * Known central nervous system (CNS) disease, except for treated brain metastasis. Treated brain metastases are defined as having no evidence of progression or hemorrhage after treatment and no ongoing requirement for dexamethasone, as ascertained by clinical examination and brain imaging (magnetic resonance imaging \[MRI\] or computed tomography \[CT\]) during the screening period. Anticonvulsants (stable dose) are allowed. Treatment for brain metastases may include whole brain radiotherapy (WBRT), radiosurgery (RS; gamma knife, linear accelerator \[LINAC\], or equivalent) or a combination as deemed appropriate by the treating physician * Patients with CNS metastases treated by neurosurgical resection or brain biopsy performed within 3 months prior to day 1 will be excluded * Current, recent (within 4 weeks of the first infusion of this study), or planned participation in an experimental drug study other than this study * Pregnancy (positive pregnancy test) or lactation * Active malignancy, other than superficial basal cell and superficial squamous (skin) cell, or carcinoma in situ of the cervix, within last five years * Inability to comply with study and/or follow-up procedures * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, or psychiatric illness/social situations that would limit adherence with study requirements