I know this is my first post, but I saw this and had to reply. I did read your entire encounter.
I know there are other people here that have more experience than me, but I just want to tell you what I think.
From what you have said she obviously likes you, and you like her. I know it may be overwhelming at first, especially with a beautiful girl for the first time. But you need to try to not be too over the top. Contain yourself for now, just try to be a nice guy. She likes you for who you are, I'm betting that she knows you are shy and that's something she likes about you. Use it to your advantage.
Do not question yourself. She can read you better than you think. She obviously thinks your a worthwhile person, and that's all that matters. You need to stop thinking so much and just go with it.
Don't worry about not being able to drive, don't worry if you don't think that you're cool enough to be with her. Just be a nice guy. That's all she really wants. Just try to be sweet and caring and be a good friend for now. If you can do that then I am betting that you are way ahead of any of the other guys she hangs out with. Honestly, alot of guys these days are a**holes (I can be as well sometimes).
Don't hesitate to tell her that this is a new experience for you. At first you need to be somewhat vague. Like I said, for now you need to just be friendly. If it develops, it will do so. It is all about timing. You need to wait for the right moments, and believe me, they will come.
Three rules:
1. Smile alot
2. Try not to become obsessed.
3. Just go with it, don't underestimate yourself.