Bleach and products containing bleach will generally remove the stain left by mold. But the mold has not been killed. To kill the mold you must use a mold killer such as Moldex. Home Depot sells a couple of them. Once the mold is dead you can use chlorine bleach to remove the stains. If you cannot completely get rid of the mold, have the grout replaced. If you remove some tile and find mold on the drywall or cement board you need to hang new cement board.
Now that you have gotten rid of it, this is the most important thing. After every shower dry yourself then use your towel to completely dry out your shower. Clean your shower with a cleaner that has bleach in it or just spray it down with peroxide twice a month just for insurance. You will not have a mold problem again. I also clean mine with Scrubbing Bubbles weekly to remove any soap scum and to disinfect.
We all have things we can’t stand. One of mine is mold in the shower. Beware…........it is not always black; it might be pink, grey, or brown. But it’s all mold and must be destroyed.