I wanna hang with this person! HELP?

[sca]

Ok I am 18 years old and I go to a University at my home town. This girl comes to this university I go to from a different state. Me and her are the same nationality and the same religion. It has been 3 months since I have known her. I just want us to be just friends. We have seen each other on random times walk in the University but it has been like three weeks and I have not seen her anymore. All I want to is increase the conversation which would increase the friendship. I dont know what to do. I still don't have her cell number which means that friendship is weak.
I dont know what to do. I need help!
Now through facebook chat, not chat throught wall on wall, just the live chat, I want to ask her if we can have lunch together if she is bored and has nothing to do.
I want a good friendship.
Is it ok to ask her to go to lunch with me through facebook or should I ask her in person?