Paclitaxel, Nab-paclitaxel, or Ixabepilone With or Without Bevacizumab in Treating Patients With Stage IIIC or Stage IV Breast Cancer

Inclusion Criteria:

* Histologic confirmation of invasive cancer of the breast
* Stage IV disease or stage IIIC disease (using American Joint Committee on Cancer \[AJCC\] criteria, 6th edition) not amenable to local therapy
* Patients may not have a "currently active" second malignancy other than non-melanoma skin cancers; patients are not considered to have a "currently active" malignancy if they have completed therapy and are considered by their physician to be at less than 30% risk of relapse
* Patients with human epidermal growth factor receptor 2 (HER2) negative disease are eligible; patients with HER2+ disease are eligible providing they have previously received trastuzumab or lapatinib; documentation of progression on HER2 directed therapy is not required; Her2/neu status must be known at the time of protocol registration
* Estrogen receptor (ER) and progesterone receptor (PgR) status must be known at the time of registration; ER and/or PgR \>= 1% cells will be considered positive
* Prior treatment may include adjuvant or neoadjuvant taxane, however, the interval between completion of adjuvant or neoadjuvant therapy and disease recurrence must be \>= 12 months
* No prior chemotherapy for metastatic breast cancer
* Any number of prior hormonal therapies are allowed; the last dose should have been administered at least 7 days prior to the initiation of protocol therapy
* Prior radiotherapy must be completed at least 2 weeks prior to study entry
* Treatment with bisphosphonates is allowed and recommended as per American Society of Clinical Oncology (ASCO) guidelines
* Prior trastuzumab or lapatinib required for patients with HER2 overexpressing tumors
* Prior treatment with bevacizumab is allowed
* Patients must not have had a major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to study registration, and must have fully recovered from any such procedure

  * The following are not considered to be major procedures: thoracentesis, paracentesis, port placement, laparoscopy, thoracoscopy, bronchoscopy, endoscopic ultrasonographic procedures, mediastinoscopy, skin biopsies, incisional biopsies and routine dental procedures
* Patients must not have anticipation of need for a major surgical procedure during the course of the study
* There are no restrictions on core biopsies, placement of a vascular access device or other minor procedures prior to registration

  * Placement of a vascular access device after starting study therapy should be performed between day 15 and 28 of a treatment cycle (but not less than 48 hours before the next dose of bevacizumab) to allow for sufficient healing
* Patients must have measurable disease (target lesions): measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 2.0 cm with conventional techniques or as \>= 1 cm with spiral computed tomography (CT) scan

  * Lesions that are considered non-measurable include the following:

    * Bone lesions
    * Leptomeningeal disease
    * Ascites
    * Pleural/pericardial effusion
    * Inflammatory breast disease
    * Lymphangitis cutis/pulmonitis
    * Abdominal masses that are not confirmed and followed by imaging techniques
    * Cystic lesions
* Patients with pre-existing peripheral neuropathy \>= grade 2 are not eligible for this study
* Patients must have an Eastern Cooperative Oncology Group (ECOG) (Zubrod) performance status of =\< 1 to be eligible for this trial
* Women must not be pregnant or breast feeding; premenopausal women must have a negative serum or urine beta-human chorionic gonadotropin (Hcg)
* Patients with a history of Common Terminology Criteria for Adverse Events (CTCAE) grade \>= 3 hypersensitivity to paclitaxel or Cremophor® EL are not eligible
* Patients with a history of abdominal fistula, or intra-abdominal abscess within 6 months prior to study registration are not eligible
* Patients with a history of gastrointestinal (GI) perforation within 12 months prior to registration are not eligible
* Patients with a history of significant bleeding episodes (e.g., hemoptysis, upper or lower GI bleeding) within 6 months prior to registration are not eligible
* Patients must not have a history of clinically significant cardiovascular disease that includes the following:

  * Uncontrolled hypertension defined as systolic blood pressure \> 150 and/or diastolic blood pressure \> 90 mmHg on antihypertensive medications or any prior history of hypertensive crisis or hypertensive encephalopathy
  * History of myocardial infarction or unstable angina within past 6 months
  * New York Heart Association (NYHA) congestive heart failure grade 2 or greater
  * Symptomatic peripheral vascular disease
  * Significant vascular disease (e.g., aortic aneurysm, aortic dissection) or arterial thrombotic events
* Patients on full dose anticoagulants must be on a stable dose of warfarin, or be on a stable dose of low molecular weight (LMW) heparin; patients receiving anti-platelet or on daily prophylactic dose aspirin are eligible, as are patients receiving stable doses of anticoagulation for atrial fibrillation
* Patients may not have a history of stroke or transient ischemic attack within 6 months prior to study registration
* Patients with a history of seizures must be well controlled with standard medication
* Patients must not have progressing or untreated central nervous system (CNS) metastases or leptomeningeal disease; patients with a history of resected brain metastases with stable magnetic resonance imaging (MRI) scans for 3 months including within 4 weeks of study start are eligible; patients with a history of gamma knife radiosurgery or whole brain radiation with stable MRI scans for 3 months including within 4 weeks of study start are eligible
* No serious, non-healing wound, ulcer or bone fracture
* Life expectancy of \>= 12 weeks
* Granulocytes \>= 1,500/ul
* Platelet count \>= 100,000/ul
* Creatinine =\< 2.0 mg/dL
* Bilirubin \< 1.5 mg/dL (unless due to Gilbert's syndrome)
* Transaminases (aspartate aminotransferase \[AST\], alanine aminotransferase \[ALT\]) =\< 2.5 x upper limit of normal (ULN)
* Serum or urine beta-Hcg negative in premenopausal women of child-bearing potential
* Urine protein =\< 1+ protein\* or urine protein: creatinine ratio (UPC) \< 1

  * Patients discovered to have \>= 2+ proteinuria at baseline must undergo a 24-hour urine collection that must demonstrate \< 1 g of protein/24 hr or UPC ratio =\< 1 to allow participation in the study