It sounds like Bully's main problem is that he thinks he is the alpha. When deciding who should be top dog, Bully or Harley, the answer is easy. Neither! The human is the alpha, dogs are the followers (equal pack members). All five of my dogs are of equal status. They do activities together to help maintain a pack mind set. I walk them all together, feed them side by side, they sleep together, etc.
When introducing them (as said in a previous post) do not bring them face to face. Take them for looooonnnnggg walk together (at least an hour or two). Also, you might want to use a basket muzzle on Bully, at least for the walk, since you don't know how he is going to act. When you get home, start setting the ground rules at the door. They both have to wait for you to enter and then invite them in. Remember everything is yours, and you get to decide what they do and what they get and when they get it. Do not allow Bully free roam. Make him follow your lead. You can invite him into each new room as you come to it, and set up boundaries where you don't want him to go.
I would separate them for a while when you aren't home or paying attention to them. Also, refrain from being to emotional with him for the first couple of weeks. Don't get excited when you meet him, and don't approach him. Make him come to you (you are the alpha), and then ignore him. As Cesar says, "no talk, no touch, no eye contact". Simply take his leash and lead him (make sure is following you not leading you). This walk will help establish your role as leader. Do this first walk without Harley. Once Bully accepts you as the leader, he will be more willing to accept other members of the pack. When they meet correct any dominant or aggressive behavior (i.e. hackles up, tail erect, ears forward, bared teeth, mounting, etc.)
Okay, back to the don't get emotional (excited, affectionate, etc.) with him. He should have to earn everything (as should Harley) affection, food, treats, etc. Dogs to not follow emotional, unstable, norotic, angry, etc. pack leaders. They only follow a calm-assertive, confident pack leader.
Hopefully some of this made sense. Since I am at work and helping customers in between sentences. And I as my husband says "I have the tendency to shift gears without pressing the clutch first".