Plerixafor (AMD3100) and Bevacizumab for Recurrent High-Grade Glioma

* This study is organized into cycles. Each cycle lasts four weeks (28 days). Cycles occur back to back without a break in between. * Plerixafor is given as subcutaneous injection (under the skin). The injection should be given at approximately the same time each day (If participants would like the option to administer their Plerixfor in the evening rather than in the morning on non-clinic days, this is a possibility, provided certain conditions are met). The research doctor will specify which days participants should take plerixafor. In general, plerixafor will be given once daily during the first three weeks of every cycle (during part 3, patients will receive plerixafor the last week of each cycle, as well). For the first week (5-7 days) of Cycle 1, the injections will be given in the clinic and the nurses will teach the participant and their spouse/friend/family member how to administer the injections. * Bevacizumab (10 mg/kg) will be given as an infusion on Days 1 and 15 of each cycle. * During Part 1 the investigators are looking for the highest dose of the study drug that can be administered safely in combination with bevacizumab so not everyone who participates will receive the same dose of the study drug. The dose given will depend upon on the number of participants who have been enrolled and how well they have tolerated their doses. * During Part 2, before patient begins their post-surgical cycles of treatment, plerixafor will be administered daily for 5-9 days at the MTD established in Part 1 of the study; patient will continue to surgery; and once recovered from surgery, patient will begin post-surgical cycles of treatment (plerixafor and bevacizumab) at the MTD/regimen established in Part 1 of the study. * In addition to taking the study medication, participants will have the following tests and procedures done: physical and neurological exam, assessments of the tumor by MRI or CT scan, routine and research blood tests, routine urine tests, pregnancy test (if applicable), ECG, collection of cerebrospinal fluid (CSF) via spinal tap. * Participants may remain in this research study as long as their tumor is responding or it is determined that receiving further study drugs will not be safe.