Erlotinib Hydrochloride and Bevacizumab in Treating Patients With Stage IV Breast Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed carcinoma of the breast with metastatic (stage IV) disease that is currently stable or progressing after therapy * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral computed tomography (CT) scan * Patients must have either stable disease or disease progression on or after therapy with one or two conventional chemotherapy regimens for the treatment of metastatic (stage IV) breast cancer * Prior treatment with high-dose chemotherapy and autologous stem cell/bone marrow transplantation is allowed, and is considered one prior regimen when administered for metastatic disease * There is no restriction for the number of prior hormonal therapies or immunotherapies * If human epidermal growth factor receptor 2 (Her2)/neu-positive (defined as 3+ by immunohistochemistry \[IHC\] or positive by fluorescence in situ hybridization \[FISH\]), prior therapy with trastuzumab required * Any number of prior regimens of chemotherapy and/or hormonal therapy are allowed in the adjuvant setting, and do not count towards prior therapy when determining eligibility for this trial * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Life expectancy of greater than 3 months * Leukocytes \>= 3,000/ul * Absolute neutrophil count \>= 1,000/ul * Platelets \>= 75,000/ul * Total bilirubin within normal institutional limits * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\[) =\< 2.5 X institutional upper limit of normal * Creatinine within normal institutional limits OR creatinine clearance \>= 60 mL/min for patients with creatinine levels outside institutional normal using the Cockcroft-Gault formula * Women of childbearing potential must agree to use adequate contraception (barrier method of birth control) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Patients must have breast cancer tissue available as either paraffin blocks or unstained slides for planned correlative science sub study * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy, radiotherapy immunotherapy or investigational therapy within 3 weeks prior to starting treatment (6 weeks for nitrosoureas or mitomycin C), or hormonal therapy within 2 weeks prior to starting treatment * Patients may not be receiving any other investigational agents * History or evidence upon physical examination of central nervous system (CNS) disease (e.g., primary brain tumor, seizures not controlled with standard medical therapy, any brain metastases, or history of stroke); all subjects must have a baseline CT or magnetic resonance imaging (MRI) of the head * History of allergic reactions attributed to compounds of similar chemical or biologic composition to OSI-774 or bevacizumab * Prior treatment with kinase insert domain receptor (KDR) inhibitors (e.g. vascular endothelial growth factor \[VEGF\] Trap, Su5416, Su6668, ZD6474, PTK757, IMC-1CII) * Prior treatment with EGFR targeting therapies (e.g. ZD1839 or C225) * Major surgery, open biopsy or significant traumatic injury occurring within 28 days prior to treatment; this does not apply to indwelling catheters, which require an interval of at least 24 hours between placement of the catheter and treatment with bevacizumab * Current or recent (within 10 days prior to treatment) use of full-dose oral or parenteral anticoagulants or thrombolytic agents (except as required to maintain patency of preexisting, permanent indwelling IV catheters; for subjects receiving warfarin, international normalized ratio \[INR\] should be \< 1.5) * Chronic daily treatment with aspirin (\> 325 mg/day) or nonsteroidal anti-inflammatory medications known to inhibit the platelet function (e.g. cyclooxygenase \[COX\]-1 inhibitors) * Presence of bleeding diathesis or coagulopathy * Cumulative anthracycline and anthracenedione exposure as follows: doxorubicin \> 450 mg/m\^2; epirubicin \> 700 mg/m\^2; liposomal doxorubicin \> 550 mg/m\^2; mitoxantrone \> 140 mg/m\^2 * Proteinuria at baseline; subjects unexpectedly discovered to have \>= 1+ proteinuria should undergo a 24-hour urine collection, which must be an adequate collection and must demonstrate =\< 500 mg protein/ 24 hours to allow participation in the study * Cardiac ejection fraction (multigated acquisition scan \[MUGA\] or echocardiogram) less than the local institution lower limit of normal * Abnormalities of the cornea based on history (e.g., dry eye syndrome, Sjögren's syndrome), congenital abnormality (e.g., Fuch's dystrophy), abnormal slit-lamp examination using a vital dye (e.g., fluorescein, Bengal-Rose), and/or an abnormal corneal sensitivity test (Schirmer test or similar tear production test) * Serious, non-healing wound, ulcer, or bone fracture * Clinically significant cardiovascular disease (e.g., uncontrolled hypertension, myocardial infarction, unstable angina), New York Heart Association (NYHA) grade II or greater congestive heart failure, serious cardiac arrhythmia requiring medication, or grade II or greater peripheral vascular disease within 1 year prior to day 0 * Gastrointestinal tract disease resulting in an inability to take oral medication or a requirement for IV alimentation, or prior surgical procedures affecting absorption * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with OSI-774 * Human immunodeficiency virus (HIV)-positive patients receiving combination anti-retroviral therapy are excluded from the study * Patients with recent (within 6 months) arterial thrombotic events, including transient ischemic attack (TIA), cerebrovascular accident (CVA), unstable angina, myocardial infarction (MI), or clinically significant peripheral artery disease