Answer: While bleach will certainly kill the moss, it doesn't cure the underlying problems which are why the moss is growing there in the first place. Moss is a symptom of one or more problems, including poor drainage, too much shade, low fertility, compacted soil, and soil that's too acidic. If you can correct these problems, you'll have fewer moss problems.
In the garden, you can scruff the soil up every few weeks to aerate and discourage moss growth, or you can put a layer of bark chips over the bare soil. If the moss is really thick, you can peel it up. If it is just in spots, you can rake it up. Then either cultivate the soil regularly, or spread a 2" layer of mulch over the bare soil.
If you have moss in your lawn, you can temporarily stop its growth by applying lime to your lawn to counteract the acidity of the soil. A more permanent solution is to aerate the soil to alleviate compaction, trim trees to allow more sunlight to penetrate, put your lawn an a regular feeding schedule (April, June, September and early December) and change your watering schedule so the soil has a chance to drain and dry out slightly between waterings.
Best wishes with your garden!
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