How do you keep black mold out of basement shower

Better ventilation. Use the exhaust fan, install one, crack a window if there is one, even a portable fan will work. Vinegar will clean the mold.

This covers the subject of mold in basements.

https://www.youtube.com/watch?v=Ghuj61aexdc

Install and use a ceiling vent fan and

Be sure to squeegee or wipe moisture off shower walls after each use.

You may also need to use a portable dehumidifier. You can either have it drain automatically into a sink or sump pump by attaching a garden hose to it, or manually empty it as needed, which could be every day or two.

use a bathroom fan ,dehumidifier, place Damp rid all around...open any windows to dry the area outdoor put a fan on to circulate the basement.