You can use the bleach water mix to try to remove algae staining but to remove actual moss growth you are going to have to use some force. Do you actually have moss chunks growing or are you talking about the algae staining and streaks? If it is the algae staining, you can do the bleach water mix, have fun. Otherwise if its the moss, maybe lightly scrap it off or spray it off with a hose, not the old power sprayer. Then maybe the bleach water solution to try to clean it up better. IMO, I don’t monkey with it much but if it bothering you, have at it.
The zinc strips do work like a charm, except its kind of a trade off, the zinc when put on a brand new roof works great to keep the algae from forming, yet the trade off is the shiny zinc strips glaring all over your roof. More so in the first few years.