When I was a mobile groomer, had a poor dog that was infested w/fleas, that the bath water turned red.
As soon as I got home, I jumped in the shower & used tropiclean neem shampoo, the same shampoo we use for dogs. Neem really kills the fleas, or at least stuns them & they drown during the bath. It also comes in oil form. Unfortunately, I saw a flea jump off my clothes & disappear...
so mine all got frontlined. We've got to try the diatomaceous earth & dawn.