Nab-Paclitaxel and Bevacizumab Followed By Bevacizumab and Erlotinib in Metastatic Breast Cancer

Inclusion Criteria: * Have histologically confirmed invasive breast cancer that is estrogen receptor (ER) negative (=\< 10%), progesterone receptor (PR) negative (=\< 10%) and human epidermal growth factor receptor 2 (HER2) normal (=\< 10% of cells) by immunohistochemistry (IHC) or fluorescence in situ hybridization (FISH) * Be receiving first-line therapy for metastatic disease * Measurable disease by Response Evaluation Criteria In Solid Tumors (RECIST) criteria; X-rays, scans or physical examinations used for tumor measurement must have been completed within 28 days prior to registration; X-rays, scans or other tests for assessment of non-measurable disease must have been performed within 42 days prior to registration * OR non-measurable disease only, with rising serum cancer antigen (CA)15-3 or CA 27.29 or carcinoembryonic antigen (CEA) documented by two consecutive measurements taken at least 14 days apart with the most recent measurement being within 42 days prior to registration; the second CA 15-3 or CA 27.29 or CEA value must have at least a 20% increase over the first and for CA 15-3 or CA 27.29 be greater than or equal to 40 units/mL or for CEA be greater than or equal to 4 ng/mL * Subjects with brain metastases as their first site of disease recurrence may be eligible if treated by definitive radiation (stereotactic radiosurgery or whole brain) with clinically controlled neurologic symptoms for a period of 21 days prior to study treatment * Bilirubin =\< 1.5 mg/dL * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 X upper limit of normal, unless bone metastasis is present in the absence of liver metastasis * Alkaline phosphatase =\< 2.5 X upper limit of normal, unless bone metastasis is present in the absence of liver metastasis * Platelets \> 100,000 cells/mm\^3 * Hemoglobin \> 9.0 g/dL * Absolute neutrophil count (ANC) \>= 1,500 cells/mm\^3 * Creatinine =\< 1.5 mg/dL is recommended; however, institutional norms are acceptable * If of childbearing potential must have a negative pregnancy test and use an effective method to avoid pregnancy for the duration of the trial and for at least 6 months after completion of study therapy * Pre-existing peripheral neuropathy, if present, must be \< grade 2 (per Common Terminology Criteria for Adverse Events \[CTCAE\] version 3.0) * Patients must be informed of the investigational nature of this study and must sign and give informed consent in accordance with institutional standards and federal guidelines Exclusion Criteria: * Recurrent disease within 12 months after completion of adjuvant chemotherapy containing a weekly taxane * Central nervous system (CNS) metastases that are symptomatic and/or requiring steroids * Pre-existing nephritic syndrome * Serious intercurrent medical or psychiatric illness including serious active infection * Inadequately controlled hypertension (defined as systolic blood pressure \> 150 and/or diastolic blood pressure \> 100 mmHg on antihypertensive medications) * Any prior history of hypertensive crisis or hypertensive encephalopathy * New York Heart Association (NYHA) grade II or greater congestive heart failure * History of myocardial infarction or unstable angina within 6 months prior to study enrollment * History of stroke or transient ischemic attack within 6 months prior to study enrollment * Significant vascular disease (e.g., aortic aneurysm, aortic dissection) * Symptomatic peripheral vascular disease * Evidence of bleeding diathesis or coagulopathy * Major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to study enrollment 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 study enrollment * History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 6 months prior to study enrollment * Serious, non-healing wound, ulcer, or bone fracture * Proteinuria at screening as demonstrated by either: * Urine protein:creatinine (UPC) ratio \>= 1.0 at screening OR * Urine dipstick for proteinuria \> 2+ (patients discovered to have \> 2+ proteinuria on dipstick urinalysis at baseline must have a UPC ratio done that is \< 1.0 to be eligible; if the UPC ratio is \>= 1.0 then the patient should undergo a 24-hour urine collection which must demonstrate =\< 1 g of protein in 24 hours for the patient to be eligible) * Known hypersensitivity to any component of bevacizumab or to nab-paclitaxel (paclitaxel albumin-stabilized nanoparticle formulation)