I say: Don't contact her anymore via texting, facebook, etc. Make her try to talk to you and see what's going on? And then after you have a short conversation with her, like 10-15 minutes, give yourself a false time constraint and end it. Then call her a couple of days later and ask her out.
As for not having a car, so what? How far away does she live? Do you have a bike? You could ride to her house. Or, you could pick a place to meet nearby and use your bike to get there. Or, get a buddy to drop you off. Something like that. You can figure it out too.
Plus, about cutting contact and letting her contact you, it's a shit test. If she's interested, she'll contact you. If she's not, she won't and you won't be wasting any time. Good luck bro.