Mix 1 cup of bleach to 1 gallon of water and put the mixture in a large spray bottle. Be sure to wear nonporous gloves and protective eyewear when working with bleach.
Rinse the roof with a hose, removing any debris that may exist. Spray the solution onto the rubber roof, focusing heavily on the mold and mildew areas.
Allow the solution to set for 15 minutes.
Scrub the roof with a soft-bristled brush; be sure to wet the brush in the solution as the solution on the roof has dried. This will loosen any dirt in creases and make it easier to scrub.
Rinse the roof with a hose until all the solution is rinsed off. If mold and mildew persist, repeat steps 2 through 4.
Allow the roof to dry completely. Apply a thin coat of rubber-roof protectant to the entire roof. You can purchase rubber-roof protectant at RV and boat stores.