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.
You're my chorus, my refrain
The verse of my first pain