Apply the bleach solution with a garden sprayer. Let it stand on the surface for about 20 minutes, then rinse it off with spray from a garden hose. Don’t let the bleach solution stand on the roof for more than 30 minutes or so without rinsing. And don’t use a pressure washer, which can damage the shingles by removing their protective layer of asphalt granules.
If accumulations of algae or moss are heavy, at least some of it should wash off the roof surface right away with the stream from the hose. You can try brushing off algae and moss with a brush or broom with medium-stiff bristles, but don’t scrub too hard. You don’t want to separate the mineral granules from the shingles.
If chunks of algae or moss or heavy stains remain on the surface after rinsing, let the roof dry, then spray on the bleach solution again. Wait 30 minutes and rinse. Don’t worry if some staining remains after the second rinse. It should wash off over time with exposure to rain and sunlight.