I let my 12/13 year old (black hair) dye it with purple streaks. Of course it needed to be bleached first. First time I paid for it at the salon after a successful 6th grade report card. After the purple wore off, the streaks remained and she wanted to dye those blue. I helped her with a store-bought box, maybe $10. After that I warned her that she'd be paying for the store-bought dye if she wanted to do it again. I think she used birthday money one more time and the novelty wore off, along with the color. The streaks grew out over a couple of years and weren't that noticeable.
Hopefully she will remember that I was flexible and fun, at least for this instance. In all other ways I'm a conservative parent and hold a hard line on things that we value as a family. Hair color was an easy win, as were a second set of holes in her ears at 15.
Good luck!