I understand about the bleach also getting her skin lighter. And yes, waxing hurts a lot at first, but then the skin numbs up over time, and the hair starts to come in less... she is still a little young for the pain though! And I tried a removal cream once, and got TONS of blisters, and my upper lip hair isn't even that bad.
I second the finishing touch razor. It works great and won't leave any type of razor burn like using a regular razor would. It is only about $10.00 at Bed Bath and Beyond, Walmart, Walgreen's...
It runs out of batteries fast, but only requires 1, so just get a pack of batteries. If it breaks (I've replaced mine a couple of times) You can find them on sale everywhere, and it's cheaper in the long run than paying for waxes and creams and such.
http://www.vitadigest.com/finishing-touch.html?gclid=CIbc...