How old are you? I'm assuming your about 15ish?
You could always join some sort of groups at school that would entail you spending a lot of time with girls. Since you're a year away from being able to drive that limits things. You're parents probably just don't want you hooking up with girls this young. Which is fine.
Most kids that can't drive do something like getting their parents to drive them to a movie with a guy friend, and meet up with girls you want to see there. But that was more the middle school way of doing it. If you actually want to go on a real "date" with a girl and you can't drive, she can't drive, and your parents won't do it, I'd say just wait until you can drive.
But its been a long time since I've been in that situation. maybe I'm missing some of the tricks people used to do.
Maybe you could get a moped? JK