Tell her that you are interested in learning Korean, then ask her some questions about certain Korean words or sentences, have her write them down and ask her to quiz you on them next time you're on the bus together. This way you have an excuse to come talk to her every time. Also, do ask to move the study lessons to a local starbucks or something. It's great because every time you cant think of something to say, or there's an awkward silence, you can just ask another question about Korean language.
Also, ask her if she has English classes. Make sure she knows you're a native speaker and offer to help her with her homework. Maybe she will just start using you to correct her papers and stuff, but hey, you gotta start somewhere.
If you want for her to come to your house, i've noticed that Korean girls really like it when you cook for them. So when you get a little bit closer with her, offer to cook some food from your country for her. I'm sure she wont turn you down if she's at all interested in you.
Other than that, talk to her gently and clearly, don't be agressive, make her laugh, etc. etc.
It wont be harder to get close to her or even date her if you're not Korean. It will only become an issue if you want to actually be her boyfriend.
Anyway, GOOD LUCK!