The problme with bleach is that it breaks things down, not just stains but the sailcloth, stitching, any coating that is bonded to the sail.
Assuming this is a typical dacron cruising sail, not a laminate or an exotic? I'd try soaking and scrubbing (scrub brushes simply work better!) with OxiClean or a similar "oxygen bleach" instead of chlorine bleach. If that doesn't work, use a laundry detergent or laundry stain cleaner that boasts it has enzymes to dissolve grass stains. Grass and mold both being plant matter.
If that doesn't work then you're back to the chlorine bleach, keep an eye on it and don't overcook it.
Sailcare is a good idea if you don't mind the shipping & lost use time. IIRC they can also recoat the sail which also helps stabilize shape & keep it clean.