The main goals of this Phase I study are to learn about the side effects that may occur when everolimus and bevacizumab are given to children and young adults and to find the highest doses of these drugs that can be given together without causing severe side effects. Bevacizumab will be given into the vein (IV) over 30-90 minutes every two weeks and everolimus tablets will be given daily by mouth. A cycle of therapy will be four weeks.