Careful with water with bleach, it does help with the moss. It will make your roof brittle over time.
My husband has been getting up on the roof with our high powered, power washer. Before he does that he sprinkles the top of the roof with a roof moss killer. After a while the moss will turn brown then he uses the power washer to wash off being careful wearing goggles and protective clothes. If your roof is in weak shape the power washer might be too much and cause leaks. Try to find moss killer that is the safest. The moss killer will be on the ground when rinsed off. Same thing with bleach and the bleach will kill flowers and grass. Along with not being so great for our pets, so take that into consideration.
Putting moss killer on your roof in the fall might help but we get so much rain it rinses off quickly. Less chemicals the better. If you can just use the force of the water it would be better.