Um, it sounds like your neighbor needs to keep her cat inside. You should not have to be responsible for this. Tell her you're going to call animal control (or whatever the equivalent is by you) and report her for neglect if her cat keeps straying.

I'm cranky today though so YMMV.

Or you could just put a litter box on your balcony, buy better food than she gets for the cat, and bribe it into being YOUR cat...muahahahaha!