Bleach is good for killing mold, but ammonia is better for keeping it gone. Bleach kills both mold and bacteria very well, but mold and bacteria compete for food. Ammonia is more effective for eliminating mold because it kills mold better than bacteria. The bacteria that survive make it harder for the mold to return. Mind you, this is my recollection of what my mother (botanist with a doctorate in ecology) told me eleven years ago.
When I deployed to the Mid-East we were in a very high humidity environment, and everything grew mold. The dorms were a trailer park, and the plastic walls of my room would grow mold. The only cleaner we could get was bleach so we had to wipe down our rooms weekly. Within a few days you'd see it growing back. I would have killed to get my hands on some ammonia.