Chemotherapy & Bevacizumab for Human Epidermal Growth Factor Receptor 2 (HER2)/Neu-Negative Stage II/III Breast Cancer

Inclusion Criteria: * Histological diagnosis of invasive breast cancer: By pathologic evaluation, primary tumor must be T1-4N1-3M0 or T3-4N 0M0 that is ER/PR positive or negative and HER-2/neu negative (1+) immunocytochemistry or not amplified by Fluorescence in situ hybridization (FISH) * OR By pathologic evaluation, primary tumor must be T2N0 that is estrogen receptor (ER), progesterone receptor (PR) and HER-2neu negative * Women of reproductive potential must be non-pregnant and non-nursing and must agree to employ an effective barrier method of birth control throughout the study and for up to 6 months following treatment * Women of child-bearing potential, must have a negative pregnancy test within 7 days of initiating study (no childbearing potential is defined as age 55 years or older and no menses for two years or any age with surgical removal of the uterus and/or both ovaries) * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Definitive surgery, lumpectomy and axillary sampling or modified radical mastectomy * Three weeks since last surgery other than port or right atrial catheter placement * No significant cardiac disease and a normal left ventricular ejection fraction * No significant open wounds, uncontrolled hypertension, history of venous or arterial clotting * Adequate laboratory parameters within 30 days prior to enrollment defined as: * Absolute neutrophil count greater than or equal to 1,500/mcl * Platelet count equal to or greater than 150,000/mcl * Hemoglobin \>11gm/dl * Alkaline phosphatase equal or less than 1.5 times the upper limit normal (ULN) * Total bilirubin equal to or less than 1.5 times the ULN * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) no greater than 1.5 times the ULN * Creatinine less than 1.5 times the ULN * Urine protein \< 2+ on urinalysis, UPC 1.0 or 24 hour urine \< 1 g protein * No active serious infections or other condition precluding chemotherapy * Able to give informed consent * Able to return for treatment and follow-up on the specified days Exclusion Criteria: * Prior malignancy; except for adequately treated basal cell or squamous cell skin cancer or noninvasive carcinomas, or other cancer from which the patient has been disease free for 5 years * Prior chemotherapy or radiation therapy * Breast cancer that over expresses Her-2/neu * Stage IV or metastatic breast cancer * Inability to cooperate with treatment protocol * Any comorbidity or condition which, in the opinion of the investigator, may interfere with the assessments and procedures of this protocol * 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 12 months of study enrollment * Any history of stroke or transient ischemic attack at any time * Significant vascular disease (e.g., aortic aneurysm, aortic dissection) * Symptomatic peripheral vascular disease * Evidence of bleeding diathesis or coagulopathy * 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 urinalysis for proteinuria \>= 2+ (patients discovered to have \>= 2+ proteinuria on urinalysis at baseline and undergo a 24 hour urine collection and demonstrate \> 1g of protein in 24 hours are ineligible) * Known hypersensitivity to any component of Avastin or gemcitabine or other required drugs in the study * History of venous or arterial thrombosis * Current, ongoing treatment with full-dose warfarin or its equivalent (i.e., unfractionated and/or low molecular weight heparin) for any reason (ASA okay)