Docetaxel and Prednisone With or Without Bevacizumab in Treating Patients With Prostate Cancer That Did Not Respond to Hormone Therapy

Inclusion Criteria: * Patients must have histologically documented adenocarcinoma of the prostate with progressive systemic (clinically metastatic disease documented on bone, CT or MRI scan) disease despite castrate levels of testosterone due to orchiectomy or LHRH agonist; castrate levels of testosterone must be maintained * All eligible patients must have a Gleason sum based on biopsy or TURP at the time of registration * At the time of enrollment, patients must have evidence of progressive metastatic disease, either: * Measurable disease with any level of serum PSA OR * Non-measurable disease with PSA ≥ 5 ng/ml; patients with PSA ≥ 5 ng/ml only and no other radiographic evidence of metastatic prostate cancer are not eligible * Definition of Measurable Disease/Target Lesions: * Any lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as ≥ 20 mm with conventional techniques: 1) physical exam for clinically palpable lymph nodes and superficial skin lesions, 2) chest X-ray for clearly defined lung lesions surrounded by aerated lung OR those lesions measured as ≥ 10 mm with a spiral CT or MRI scan * Measurable lesions (up to a maximum of 10 in number) representative of all organs involved to be identified as target lesions; the sum of the longest diameters (LD) for all target lesions will be calculated and reported as baseline sum LD * If measurable disease is confined to a solitary lesion and is not consistent with prostate cancer, then its neoplastic nature must be confirmed by histology * Ultrasound may not be used to measure tumor lesions that are not easily accessible clinically * Definition of Non-measurable Disease/Non-target Lesions: * Non-target lesions include all other lesions not included in above, including small lesions with longest diameter \< 20 mm with conventional techniques or \< 10 mm with spiral CT scan and truly non-measurable lesions, which include: * Bone lesions * Pleural or pericardial effusions, ascites * CNS lesions, leptomeningeal disease * Irradiated lesions, unless progression documented after RT * Patients must have demonstrated evidence of progressive disease since the most recent change in therapy; progressive disease is defined as any one of the following (measurable disease, bone scan, or PSA progression): * Measurable Disease Progression: Objective evidence of increase \> 20% in the sum of the longest diameters (LD) of target lesions from the time of maximal regression or the appearance of one or more new lesions * Bone Scan Progression: Appearance of one or more new lesions on bone scan attributable to prostate cancer along with a PSA ≥ 5 ng/ml will constitute progression * PSA Progression: An elevated PSA (≥ 5 ng/mL) which has risen serially on at least two occasions after the discontinuation of antiandrogen therapy, each at least one week apart; if the confirmatory PSA (#3) value is less than screening PSA (#2) value, then an additional test for rising PSA (#4) will be required to document progression * The reference PSA value (#1) must be measured at the time of the discontinuation of antiandrogen therapy; and at least 2 PSA measurements must be made following the end of antiandrogen therapy and prior to registration * (For the purposes of the nomogram calculator, the last PSA value recorded prior to the initiation of treatment will be considered the baseline PSA) * Progression despite standard androgen deprivation therapy (i.e., LHRH agonist and/or orchiectomy) * All antiandrogens (e.g., flutamide, megestrol acetate \[even if taken for hot flashes\], bicalutamide and nilutamide) of any dose must be discontinued at least 4 weeks prior to registration; if improvement following antiandrogen withdrawal is noted, progression must be established using the criteria above * Primary testicular androgen suppression (e.g., with an LHRH agonist) should not be discontinued * At least 4 weeks since any other hormonal therapy, including ketoconazole and aminoglutethimide; the only exception to this time frame is that 5α-reductase inhibitors (e.g., finasteride, dutasteride) may be discontinued any time prior to registration * No prior cytotoxic chemotherapy, including estramustine or suramin * No prior anti-angiogenesis agents, including thalidomide and bevacizumab * ≥ 4 weeks since major surgery and fully recovered * ≥ 4 weeks since any prior radiation (including palliative) and fully recovered * ≥ 8 weeks since the last dose of Strontium-89 or Samarium * Patients receiving a bisphosphonate must be on a stable dose and must have started the bisphosphonate ≥ 4 weeks prior to initiating protocol treatment. Patients do not have to be on a bisphosphonate to qualify for the study; patients may initiate bisphosphonate therapy after completion of Cycle 1, if clinically indicated * Patients enrolled on CALGB 90202 who have documented disease progression and have received at least 4 weeks of open label zoledronic acid treatment, are eligible for this study. * No known brain metastases (brain imaging (MRI/CT) is not required) * No current congestive heart failure (New York Heart Association Class II, III or IV) * Patients with history of hypertension must be well controlled (\< 160/90) on a regimen of anti-hypertensive therapy * Patients on full-dose anticoagulants must be on a stable dose of warfarin and have an in-range INR (usually between 2 and 3) or be on a stable dose of LMW heparin; patients receiving anti-platelet agents are also eligible; in addition, patients who are on daily prophylactic aspirin or anticoagulation for atrial fibrillation are eligible * No significant history of bleeding events or GI perforation * Patients with a history of significant bleeding episodes (e.g., hemoptysis, upper or lower GI bleeding) within 6 months of registration are not eligible * Patients with a history of GI perforation within 12 months of registration are not eligible. * No recent (within 12 months) arterial thrombotic events, including transient ischemic attack (TIA), cerebrovascular accident (CVA), unstable angina or angina requiring surgical or medical intervention in the past 12 months, or myocardial infarction (MI); patients with clinically significant peripheral artery disease (i.e., claudication on less than one block) or any other arterial thrombotic event are also ineligible * No serious or non-healing wound, ulcer or bone fracture * No peripheral neuropathy ≥ grade 2 * Patients with known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies are not eligible * PC-Spes, Saw Palmetto, and St. John's Wort must be discontinued before registration; the discontinuation of other herbal medications and food supplements is strongly encouraged; patients may continue on daily vitamins and calcium supplements * ECOG performance status: 0-2 * ANC ≥ 1500/μL * Platelet count ≥ 100,000/μL * Creatinine ≤ 1.5 x upper limits of normal * Bilirubin ≤ 1.5 x upper limits of normal * For patients with Gilbert's Disease, ≤ 2.5 X ULN is allowed * AST ≤ 1.5 x upper limits of normal * PSA ≥ 5 ng/mL (if non-measurable disease) * Urine protein to creatinine ratio \< 1.0