Do not use bleach on asphalt shingles in any concentration! Although it will kill moss instantly, it may also cause discoloration of shingles surface, contaminate soil in a downspout area, and eventually kill all the plants nearby the downspout(s).
There’s a good recipe on ehow.com
for a homemade, organic moss killer.
Before any attempts of cleaning the roof make sure you prepare everything so it’s safe to climb and perform work on your roof: securing the ladder, using safety harness and ropes.
The following are 3 paragraphs from the above mentioned website and you may want to check all the instructions from their website.
Make your own organic moss killer by pouring hydrogen peroxide in a power spray container and applying it to the roof. Use white vinegar or a combination of orange juice and vinegar. Each of these formulas is alkaline and effective at killing moss over time.
Do not hose the mixture off because it sits on the moss and changes the hospitable pH factor, and that kills it over time. If it rains, reapply when the storm has passed. When the moss is brown and crumbly, hose it away.
Zinc strips are effective at killing moss. Nail in strips starting at the peak of the roof, and apply every few feet on top of the shingles. As rain falls, the zinc leaches out of the strips, flows over the moss and kills it.
Once your roof is clean, trim trees that overhang the roof, and make sure that the sun can reach the roof. Sunlight is an effective way of eliminating moss and algae, especially in a humid climate.
Remember: Safety First!