Dealing with Dragons — Patricia C. Wrede

Princess by Birth. Adventurer by Choice.

Meet Princess Cimorene -- a princess who refuses to be proper. She is everything a princess is not supposed to be: headstrong, tomboyish, 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 around. Of course, Cimorene has a way of hooking up with dangerous characters, and soon she's coping with a witch, 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!