Grass is the only mulch I use on my veggie and herb beds. I did a 2" layer today. Start with a 2" layer. The next mowing add 2" more. Maintain no more than a 4" layer. 2-3" works for my soil. Since you use compost 2" may do for you. Make sure the grass has not been treated with anything within the past two weeks of using. Mow grass and spread it immediately. Keep mulch 2" away from seedling
stems. Grass will turn a color similar to straw. Reapply as needed thru the season.
Move mulch away from the drip line of the pepper
plant every three days and check soil for moisture. If it's moist an inch or two down don't water and replace mulch. Can you find a few buckets to collect rain water for use on the veggie bed?
Avoid overfertilizing peppers
. Use fertilizer with a higher middle number-phosphorus- since peppers
(and tomatoes) bloom to set fruit. Any veggie that sets a bloom needs more phosphorus than nitrogen. If you use a higher first number- nitrogen- you get all leaves and few blooms. Its best to feed peppers
at planting time and then 5-6 weeks later. If you have a late maturing variety wait 6 weeks.
I use Garden Tone. It has a 4-6-6 ratio.