i was in a very similar situation. what stopped me from calling her was that I found out she was dating someone else already, i think if she hadn't been dating that other guy, that she would have been dropping more hints on me, because I could tell that she like me. THere is not much I can do for now though. I am going to throw a birthday party for myself at my house, and I am going to get her freind that I am also freinds with to invite her along. This is out of the ordinary for me, though, because I have never thrown a party, and I am really on the quite side of things. I have a good house for party's, though, and my sister used to throw some good ones here.
i would say in your situation, it would really help if you knew one of her freinds. I happen to know one of this girl's freinds, so i am a little lucky.
I think your best bet would be to get a group of people together to go do something, like bowling, put-put golf, anything like that. Then you could either get one of her freinds to get her to come along, or you could call her and ask her if she wants to come with. If you are with a group of people, it is less like a date, so your just "hanging out" with her. That way you could get to know her better or whatever. It can sometimes be hard to get a group of people together like that though, so good luck. It would really help if you could get one of her freinds to go on this outing, so that she will have someone that she knows better to talk to, and would feel more comfortable, and less out of place.