I love cultural differences like this. I live in the suburbs of the the biggest city in a small country, Scotland. It would be actively weird and creepy to drive someone you're going on a date with around. And you know, alcohol.
I guess that would be going off topic so I will drop it..
Anyway, guy, you didn't fuck up at all, she just sounds as nervous you, and that probably means she's into you. Decide on a time and a place and go make it happen. Just remember, a date isn't as big a deal as you're building it up to be in your head.