..." if we try to pet the Dob the bully will charge over and start growling and nipping at her legs (usually the dobe will just walk away).

.... Our bulldog is a pusher...always jumping at the doberman, growling at her in a "come get some" sort of way. The doberman is fairly passive around her, but will randomly walk up to her and start licking her (which bugs the bulldog), puts her paw on her head, etc. The doberman is clearly the alpha.,." QUOTE

Actually it sounds like the bulldog is the alpha. The alpha would "growl" at a move she didn't like by other dog, Alpha would be "eyeing" the food while eating and be ready to "charge" if the Dobe is getting attention/petted (also this shows her attempting alpha status over you, as she's now "telling you" you can't pet your dobe by running her off). Also submissive dogs are the ones to go to others and lick them. I would keep that in mind. I believe it's the bully who thinks she's the alpha, and you need to establish yourself alph over her as mentioned in previous posts.