How about -
Cha: I'm up for the car show and thanks for the offer. Can I get a lift back too and can I pitch my tent near yours?

I really wont push the boat too far in asking if you can a share tent together. You really dont know her apart from talking about cars, etc. She might be going with her bf, friends. And once you there and do a bit of game with her, she might just ask you sneak in her tent...! Good luck matey!!