Dealing with Dragons by Patricia C. Wrede

Meet Princess Cimorene--a princess who refustes to be proper. She is everything a princess is not supposed to be: headstrong, tomobyish smart...

And bored.

So bored that she runs away to live with a dragon. And not just any dragon, but Kazul--one of the most powerful and dangerous dragons arounds. Of course, Cimorene has a way of hooking up with dangerous characters, and soon she's coping with a witch,a a jinn, a death-dealing talking bird, a stone prince, and some very oily wizards.

If this princess ran away to find some excitement, it looks like she's found plenty! With a new look and new introduction from the author.