There are three things you need when cleaning a fiberglass shower: fiberglass cleaner, a white pad and a toothbrush. Most mildew will be removed via weekly cleaning. Apply fiberglass cleaner, agitate with a white pad and a toothbrush, and then rinse. This will remove soap scum and water spots, and it will also remove most or all of the mildew. If mildew remains, apply household liquid bleach solution. Use a spray bottle to do this, but adjust the nozzle so it quirts, rather than sprays, the bleach onto the mildew. This minimizes the amount of bleach in the air that you might breathe. (Also, leave a window open if you can.) Leave the room immediately after applying the bleach, close the door if you don’t appreciate bleach odor in the rest of the house, and return a few minutes later for a final rinse with cool or warm (not hot) water. Rinsing is not optional; chlorine bleach can eat away at chrome fixtures and other durable surfaces if left to its own devices. Grout, especially older grout, can begin to dissolve as well.