Yes, by all means, put some bleach in. But, since the water is so shallow, and since there's no circulation, take a 5 gallon bucket, or small garbage can, and mix 1/2 gallon of bleach into 2 - 3 gallons of water, and then pour it around the pool. Take your fill hose, and wash off the splatters. Don't do this with nice clothes on -- you're likely to spatter, and bleach is very hard on clothes if it's a little concentrated.