Well, the only advice I can give is to talk to her about it. I have found that unlike men, women like to talk about feelings and relationships. So sit down with her, tell her that you really like her alot, and that you would like to know how she feels about you. Be calm, have your thoughts orginized, and listen without prejudice to what she is saying. Do not jump to conclusions! Do not raise your voice or put her on the defensive. This relationship is in its infantsy, it is still very fragile.
If the answers about her feelings are possitive, then you can talk about when you can see her. You say that her schedule is very hectic. So get a calendar, and try and plot out when you two can get together. Be prepared, perhaps you could have 5 or 6 planned dates ready before you talk to her. Going to the zoo, movies, picnick, whatever. Then all its about is fitting them in to her schedule.
If that gos well, then you can perhaps git into her habbit of ignoring you when she is with her friends. But I might wait on that. If everything has gone well so far ending it on a sour note might not be the best idea.
At all times remain calm. If things do not go your way, do not yell or intimidate her. If you trully love this woman (three months is kinda fast, but who knows) then you do not want to create a chasm between you and her. Just remember that if it is ment to be it will happen. Just be patient. And if its not ment to be? Then its better to know sooner than later.
Hope that helped.
Shaftiel