Here in coastal South Carolina where it's damp and hot a good bit of the year, mildew and mold can be a big problem. I don't know about bleach and bluestone, but I do know that bleach is ruinous to marble. Here I'd go to Clemson University's county agent who would help me with products that have a good track record for your local problems, don't damage the environment, and are safe for you too.

My guess, something easy to dilute and biodegradable like vinegar might do the killing, then a soap to clean it. I don't have a power washer and those things can take the mortar with them.

Someone who actually knows something, please post!