Gemcitabine Hydrochloride and Docetaxel With or Without Bevacizumab in Treating Patients With Advanced or Recurrent Uterine Leiomyosarcoma

Inclusion Criteria: * Patients must have advanced or recurrent uterine leiomyosarcoma with documented disease progression; histologic confirmation of the original primary tumor is required * All patients must have measurable disease as defined by RECIST 1.1; measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded); each lesion must be \>= 10 mm when measured by CT, MRI or caliper measurement by clinical exam; or \>= 20 mm when measured by chest x-ray; lymph nodes must be \>= 15 mm in short axis when measured by CT or MRI * Patient must have at least one "target lesion" to be used to assess response on this protocol as defined by RECIST 1.1; tumors within a previously irradiated field will be designated as "non-target" lesions unless progression is documented or a biopsy is obtained to confirm persistence at least 90 days following completion of radiation therapy * Patients must have a GOG Performance Status of 0, 1, or 2 * Patients must have recovered from effects of recent surgery, radiotherapy or other therapy * Patients should be free of active infection requiring antibiotics (with the exception of an uncomplicated UTI) * Any hormonal therapy directed at the malignant tumor must be discontinued at least one week prior to first day of study treatment; continuation of hormone replacement therapy is permitted * Platelet count greater than or equal to 100,000/mm\^3 * ANC count greater than or equal to 1,500/mm\^3 * Creatinine less than or equal to 1.5 x institutional upper limit normal (ULN), per NCI CTCAE Version 4.0 Grade 1 * Bilirubin within normal range (CTCAE Version 4 Grade 0) * SGOT and alkaline phosphatase less than or equal to 2.5 x ULN, per the CTCAE Version 4.0 Grade 1) * SGOT less than or equal to 2.5 x ULN, per the CTCAE Version 4.0 Grade 1 * Alkaline phosphatase less than or equal to 2.5 x ULN, per the CTCAE Version 4.0 Grade 1 * Neuropathy (sensory and motor) less than or equal to Grade 1 per the CTCAE Version 4.0. * No history of transient ischemic attack (TIA) or stroke or CNS hemorrhage within the past 6 months * Urine protein creatinine (UPC) ratio must be \< 1.0 gm; if UPC ratio \>= 1, collection of 24-hour urine measurement of urine protein is recommended * PT such that international normalized ratio (INR) is =\< 1.5 and a PTT =\< 1.5 times the institutional upper limit of normal (or an in-therapeutic-range INR, usually between 2 and 3, if a patient is on a stable dose of therapeutic warfarin) * Patients must have signed an approved informed consent and authorization permitting release of personal health information * Patients must meet pre-entry requirements * Patients of childbearing potential must have a negative serum pregnancy test prior to the study entry and be practicing an effective form of contraception Exclusion Criteria: * Patients who have received prior cytotoxic chemotherapy for management of uterine sarcoma; patients who have received prior VEGF-pathway targeted agent such as bevacizumab, PTK787, VEGF-trap, or who have received prior treatment with a multi-kinase inhibitor such as sorafenib or sunitinib are not eligible * Patients who have had prior therapy with docetaxel or gemcitabine or bevacizumab * Patients with a history of other invasive malignancies, with the exceptions of non-melanoma skin cancer, carcinoma in situ of the cervix, and ductal carcinoma in situ of the breast, are excluded if there is any evidence of other malignancy being present within the last five years; patients are also excluded if their previous cancer treatment contraindicates this protocol therapy * Patients with active bleeding or pathologic conditions that carry high risk of bleeding, such as known bleeding disorder, coagulopathy, or tumor involving major vessels; (necessary use of warfarin or low molecular weight heparin is permitted, provided the INR is maintained in the therapeutic range of approximately 2-3) * Patients with major surgery or significant traumatic injury within 28 days prior to study entry * Patients with a history of abdominal fistula or perforation within the past 12 months * Patients with a current, serious, non-healing wound, ulcer, or bone fracture * Patients with history or evidence upon physical examination of CNS disease, including history of primary brain tumor, or any history of brain metastases, or seizures not controlled with standard medical therapy * Patients with known hypersensitivity to Chinese hamster ovary cell products or other recombinant human or humanized antibodies * Cardiovascular function; specifically, patient may not have: * Uncontrolled hypertension, defined as systolic \> 150 mm Hg or diastolic \> 100 mm Hg in a patient with no history of hypertension; patients with a history of hypertension before enrollment on study are permitted, but such patients must have BP less than or equal to 140/90 mmHg; use of blood pressure medications to achieve and maintain blood pressure control is permitted * Myocardial infarction or unstable angina within 6 months of the first date of bevacizumab/placebo therapy * New York Heart Association (NYHA) Grade II or greater congestive heart failure or serious cardiac arrhythmia requiring medication; women who have received prior treatment with an anthracycline (including doxorubicin and/or liposomal doxorubicin) and have an ejection fraction \< 50% will be excluded from the study * Grade 1, Category 2 or greater, peripheral vascular disease; patient cannot have anything worse than mild, symptomatic claudication with exercise * History of cerebrovascular accident (CVA, stroke), transient ischemic attack (TIA) or subarachnoid hemorrhage within six months of the first date of bevacizumab/placebo therapy * History of pulmonary embolism or deep vein thrombosis in the past 6 months * Patients with, or with anticipation of, invasive procedures as defined below: * Major surgical procedure, open biopsy or significant traumatic injury within 28 days prior to the first date of bevacizumab/placebo therapy * Major surgical procedure anticipated during the course of the study. * Minor surgical procedures (i.e., mediport insertion), fine needle aspirates, or core biopsies within 7 days prior to the first date of bevacizumab/placebo therapy * Patients who are pregnant or nursing