Bar soaps are in general more alkaline compared to the pH of a dogs skin so it may strip the coat and irritate the skin. This company is a very good one though so not sure what the pH of the soap is.
I have found the foaming face washes by Nature's Specialty and Show Seasons to be my favorite by far. They can be used wet or dry, meaning you can use it as a spot treatment for stinky faces and don't have to rinse it off.
Plum Crazy foaming face wash for dogs and cats and pets by Natures specialties Natural Pet Shampoos and Groomer Products - Natures Specialties Manufacturing 2.5 oz. Face TimeŽ Foaming Face Wash - Specialty - ShowseasonŽ Product Line