Hmm, good question. I'm not sure baby shampoo has soap as such in it - otherwise how do they make it "no more tears" because soap sure as heck stings your eyes. But it must dissipate oil off your hair somehow. Ok, got my Burt's Bees Baby shampoo label, but we may need Rick or some other chemist to tell us if these ingredients will kill bugs. Take a look at your label, it may be different than mine. My dish soap label has a few ingredients in common, but not the leading ones.
Maybe mix some up in a little spray bottle and try it? Next time you spot a wasp or something you don't mind murdering?
Dish soap works great on wasps, btw.