It's dish soap yes, but it is also the soap that Tri-State Bird Rescue and Research — one of the premier wildlife response organizations in the U.S. uses as well! My Momma always uses the blue dawn dish soap on me. And always a pea size (or two).
In case you are wondering when the first time your bath should be, it is once you've reached seven months of age. Also it is not ideal to take a daily bath so make sure your pawrents only bathe you once a month or even better every other month to help keep your coat nice and shiny!
Enjoy your bath!