Peroxide technically is bleach, but on its own it can lighten, and since her hair isn't a super light color, it'd probably be safer to do that so that you don't go too light. It'll still be drying but not as much.
There are tutorials on youtube, but if you just spray peroxide on your hair and leave it in overnight, and maybe redo it another time or two if you have to, I've seen people get results. also mixing honey with your conditioner, because it's a lightening agent. and the henna you already have should help with the red hue