you know your mom and what makes her tick better than i do, of course... but here are my suggestions:
if you don't want to bug her and ask her constantly, maybe think about writing her a letter? that way, she can read it when she has time. (sometimes moms are a lot busier than you think they are ;) )
If you'd rather talk to her, i'd approach her and pick a time and date to sit down with her and really discuss it. it sounds silly, but setting up a meeting and choosing a time where all of her attention is on you will help. if you choose a time to discuss it, prepare yourself! if you know where you're moving - maybe look up a few gyms in the area and gather some info on them (cost, practice times, travel, etc.) while i can't tell you if she'll agree to let you cheer she'll know you're serious about it and that it's something you really want.
good luck!
