How do you remove black mold from bathoom wallpaper without removing the color from the wallpaper?

You can definitely try spraying some diluted household cleanser on it (no bleach), and rubbing the mold off with a sponge or cloth. The first priority is your safety. You should wear a dust mask while cleaning mold so that you don't breathe in the spores. And you should ventilate the area well until it is completely dry afterwards. Since mold grows readily with moisture, you should also try to increase ventilation to the bathroom in the future, to prevent future mold growth.

But keep in mind that there might be more mold than you can see. Mold can grow also on the backside of drywall and wallpaper. So if you suspect that you may have a more extensive mold problem, consider calling a mold remediation expert.