
WTF? is the right thing for you to be saying. The principal is no more responsible for you when you are biking as he/she is when your dad is driving you. If you took the bus, I can see how that might be different.
23 miles is a long way (unless you meant 2.3 or something like that). Have you ridden that far before? Have you tested out the route?
There's gotta be some place for you to lock up your bike if you're creative. Is there a lightpost in the parking lot? If so, perfect!
You can tell your principal that she is full of $H!^. Tell her BikerTeen said so. Well, maybe that's not such a good idea.

But seriously, if you would like one of us advocacy-types to email her, give us her address. I'd have no problem using my full name, address, credentials, and whatever else she wants when corresponding with her.
Bottom line: You're a brave kid for even considering riding to school. Most would be too afraid of "peer pressure," although I think you'll find that it brings positive interest and curiousness your way.
Ride if you want despite what your principal says. If she tries to get you in trouble (I doubt she will), send in the BikeForums troops ASAP! There may even be someone here who lives near you who could help your cause.
Good luck. Let me know if you need more advice or encouragement.