And if you do tell her how you feel (like ongakuka-san said, the worst thing really that could happen is that they don't return your feelings and that does hurt but time heals wounds) and she wants to just be friends, she most likely only wants to be friends (with a few exeptions).
Ask her out.. The worst she can do is say no. If she does say no then she'll know you like her, and that might make her start to like you. even if your the shyist person on earth once you get it over with it's easy. Also if she does say no you wont be feeling that way anymore, you might still like her but you wont shake and whatever. If she says yes after a few days you shouldn't shake and feel nervous around her.
I'm sorry to disagree (with the underlined words). In my humble opinion, there is a much worse thing that could happen: she says yes, it all begins well, but it ends wrong.
If I read correctly, he has to teach her Japanese. So, if by any reason it becomes uncomfortable to be around her, then everything can be far more difficult.