At one time Hinkley and Oaks gave some thought to changing the mascot to a salamander. Then law enforcement advised them that they had failed to discern that the documents they were buying from Mark Hoffman were forgeries. No salamander mascot.
If you mean the one in this catalog, I think that the image is supposed to be of a cougar, not a bulldog, although I can certainly see why you'd get 'bulldog' out of just glancing at it.