Fludarabine Phosphate, Rituximab, and Bevacizumab in Treating Patients With B-Cell Chronic Lymphocytic Leukemia That Has Relapsed or Not Responded To Treatment

Inclusion

* Relapse or refractory chronic Lymphocytic leukemia as defined by the WHO criteria and exhibit active disease requiring treatment as per the NCI working group in CLL
* Disease measurable defined by a combination of lymphocytosis \>= 5,000/mm\^3 in peripheral blood and lymphocytosis \>= 30% in bone marrow
* Confirmed CD20 expression on malignant CLL cells
* ECOG performance status of 0-2
* Life expectancy of at least 6 months
* Documented negative serologic testing for human immunodeficiency virus (HIV), hepatitis B (unless serologically positive due to prior vaccination), and hepatitis C within the year prior to enrollment
* Aspartate aminotransferase (AST) \< 2.5 x upper limit of normal (ULN)
* Total serum bilirubin \< 2.5 x ULN
* Serum creatinine \< 1.5 x ULN
* Hemoglobin \> 8 g/dL
* Absolute neutrophil count (ANC) \> 1,000 cells/mm\^3
* Platelet count \> 50,000/mm\^3
* PT/INR and PTT \< 1.5 x ULN
* Within 2 weeks prior to registration, patients must have had a urinalysis negative for protein or a 24-hour urine collection demonstrating \< 500 mg protein
* If female and of child-bearing potential, have a negative serum pregnancy test within 14 days of enrollment
* If sexually active male or sexually active female of reproductive capability, has agreed to use a medically accepted form of contraception from time of enrollment to completion of all follow-up study visits
* Signed an institutional review board (IRB)-approved informed consent document for this protocol

Exclusion

* Patients must not require sustained support of hematopoietic cytokines or transfusion of blood products
* Presence of acute infection or other significant systemic illness
* Central nervous system involvement by malignancy, history of CVA, or seizure
* Previously received Bevacizumab
* Received transplant or Alemtuzumab within 3 months of enrollment
* Received an investigational agent, systemic corticosteroids, chemotherapy, immunotherapy, biologic therapy, antibody therapy (e.g., Rituximab) and/or radiation therapy within one month of enrollment
* Radiation to \> 25% of bone marrow or any radiation therapy within 4 weeks prior to start of therapy
* Inability to comply with study and/or follow-up procedures
* Life expectancy of less than 6 months
* Fludarabine-refractory disease (no response of disease to \>= 3 cycles of a fludarabine-based regimen or relapse within 6 months of fludarabine-based regimen)
* Current, recent (within 4 weeks of the first infusion of this study), or planned participation in an experimental drug study other than a Genentech-sponsored bevacizumab cancer study
* Patients with prior malignancy other than lymphoma, except for adequately-treated skin cancer (basal cell or squamous cell carcinoma), in situ cervical cancer, or other cancer for which the patient has been disease-free for 5 years unless approved by the PI
* Inadequately controlled hypertension (defined as systolic blood pressure \> 150 mmHg and/or diastolic blood pressure \> 100 mmHg)
* 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 Day 1
* History of stroke or transient ischemic attack within 6 months prior to Day 1
* Known CNS disease, except for treated brain metastasis; Patients with CNS metastases treated by neurosurgical resection or brain biopsy performed within 3 months prior to Day 1 will be excluded
* 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
* Evidence of bleeding diathesis or significant coagulopathy (in the absence of therapeutic anticoagulation)
* 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 minor surgical procedure, excluding placement of a vascular access device, within 7 days prior to Day 1
* History of abdominal fistula or gastrointestinal perforation within 6 months prior to Day 1
* Serious, non-healing wound, active ulcer, or untreated bone fracture
* Proteinuria as demonstrated by a UPC ratio \>= 1.0 at screening
* Known hypersensitivity to any component of bevacizumab
* Pregnancy (positive pregnancy test) or lactation; use of effective means of contraception (men and women) in subjects of childbearing potential