Start with a mild soap solution and warm water. Rub it in with a soft brush, let it sit a few minutes (but don't let it dry), rinse it off and see if that worked. If not, get a canvas cleaner made for mold that isn't bleach ased. Follow directions and see if that works. The key is to not go directly to the heavy duty stuff if it isn't needed.
Once the cover is dry, you may want to coat it with a fabric treatment. 303 Protectorant for fabrics works well but is expensive,
I have also used Starbrite water repellent for my older canvas. It helps the cover shed water and helps reduce both dirt and mold buildup in the material.
Going forward, the cover should be rinsed frequently to wash off dirt. Once it stops shedding water, it is time for another treatment.