Yeah, ask her. I know it can be a hard thing to do, but you never get anything in life without taking chances. Nothing really bad can happen anyway. Getting turned down might be a blow to your dignity, but there's not much in life that doesn't put your dignity at risk.

But, um, don't get your hopes up too much. If you're seriously thinking of asking her, I can only assume you have some reason for thinking you have a chance. It's just that it's a little odd regardless, you know? It's not the kind of thing that happens often. Even if (going hypothetical here) she'd secretly liked you since she started teaching you, she would still be suprised to be asked.

Still, I highly recommend doing it no matter what you think of your chances, just so you can say you did. The way I look at it, doing things that a lot of people wouldn't even think about is a sure way to have an interesting life.