Yes you can use household bleach it will take a lot to do depending on the size of the roof being treated. For example the last roof I did was about 3000 Sqft and it took me about 40 gal SH to complete. It was pretty bad and required additional treatments in a few areas. I used a 50/50 mix with my proportioner which was about a 6% solution once it came out of the gun. I use 12.5% SH we get ours from a chemical distributer in Houston. They are the best for keeping costs down and they will deliver too in certain cases. If you don't have proper equipment I would start with a 50/50 mix using what bleach you can find in a pump up sprayer with some sort of surfactant and start in a small area and do a test. Then just take your time and treat the areas that need it.