the dawn may dry out the skin a little but if you rinse with a little conditioner it will help. I had to use baby shampoo on a very old dog we had, he was allergic to any flea meds, and then used just very little people hair conditioner and rinsed very well. When you give a pet a bath you are really drowning the fleas, the meds in pet shampoo are not really that necessary (per my vet) but you cant bathe a pet 2, 3, 4 times a week so they suggest something like Frontline.
I cant express how treating the rest of the house is important, something as simple as vaccuming everything and then tying the vac bag up in a plastic/ziploc and throwing it out. This will help pick up the eggs and loose fleas in bedding and carpet.