Iodine I 131 Monoclonal Antibody 3F8 and Bevacizumab in Treating Patients With Relapsed or Refractory Neuroblastoma

Subject Inclusion Criteria: * Patients must have the diagnosis of NB in accordance with the International Criteria, i.e., either histopathology (confirmed by the MSKCC Department of Pathology) or BM involvement plus elevated urinary catecholamines. * Must have a history of tumor progression or recurrence or failure to achieve complete response with standard therapy. * Patients must have evaluable (microscopic marrow metastasis, MIBG or PET scans) or measurable (CT, MRI) disease. * Prior Therapy: At least 2 weeks should have elapsed since any biologic therapy. Three weeks should have elapsed since last dose of chemotherapy or radioimmunotherapy. * Age \>1 year and able to cooperate with radiation safety restrictions during therapy period. * Stem cells: Patients must have an autologous hematopoietic stem cell product cryopreserved and available for re-infusion after MIBG treatment. The minimum dose for hematopoietic stem cells is 2 X106 CD34+ cells/kg. * Minimum life expectancy of four weeks. * Signed informed consent indicating awareness of the investigational nature of this program. Subject Exclusion Criteria: * Severe major organ toxicity. Renal, cardiac, hepatic, pulmonary, gastrointestinal and neurologic toxicity should all be grade 2 or less (per NCI CTC version 3 criteria). Specifically, serum creatinine should be ≤3 x upper limit of normal (ULN), serum AST and ALT ≤5 x ULN, serum bilirubin ≤ 3 x ULN, LV shortening fraction should be ≥15%. * Patients with myelosuppression are not excluded if ANC ≥ 500/uL. Platelet count should be \> 50,000/ul and hemoglobin should be \> 8gm/dl. Patients may receive platelet or red blood cell transfusions to maintain hemoglobin and platelets at clinical appropriate levels. * Patients with documented chronic non-healing wound, ulcer or bone fracture * Surgical procedures. * Patients who have undergone major surgery \<28 days prior to beginning therapy with bevacizumab are excluded. * Patients must be least 24 hours from having after surgical procedures such as placement of central catheter. * Patients \<7days from minor surgeries (e.g. fine needle or core biopsies) and/or the unhealed wounds from these procedures are excluded. * Patients will be excluded if major surgery (e.g. abdominal or thoracic surgery for resection of tumor) is anticipated during the course of the study. Known bleeding diathesis or coagulopathy. Patients on anti-coagulants (except for heparin flushes for centra venous catheter maintenance) are excluded. * Thrombosis: patients must not have had a deep venous or arterial thrombosis (non-central venous catheter related) within the last three months prior to study entry. Patients with cerebrovascular accident or transient ischemic attack within 6 months of therapy are excluded. Patients with history of peripheral vascular disease, myocardial infarction or unstable angina are excluded. * History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 6 months prior to study entry. * Pulmonary or CNS metastases: pre-therapy CT or MRI of head and chest must be carried out. * Proteinuria: Urine protein: creatinine ratio ≥ 1.0 * Uncontrolled hypertension. * HAMA \>1000 ELISA units/ml. * History of allergy to mouse proteins, Chinese hamster ovary cells products or other recombinant human antibodies * Active serious infections not controlled by antibiotics. * Pregnant women are excluded for fear of danger to the fetus. Therefore negative pregnancy test is required for all women of child-bearing age, and appropriate contraception is used during the study period. * Inability or unwillingness to comply with radiation safety procedures or protocol requirements.