Don't think of Enterprise as having eight (

reactors. Think of it as having four (4) dual-reactor plants. Oh, and don't let anyone tell you that they're small. It's a very powerful and flexible system. No one, as I recall was assigned to a specific reactor, except maybe the RO standing watch on it, and then there's no rule that says that he would need to be from that plant (i.e., it's a temporary assignment that only lasts the length of the watch).
As far as "Bull Nukes" go. I have no idea what you're talking about. I served on the E for six (6) years and never heard anyone referred to as the "Bull Nuke." We had several Master Chiefs in Reactor Department. One of them was the Departmental Master Chief. I never heard anyone call him the "Bull Nuke." We called him "Crusty the Clown" because of a remarkable physical and behavioral resemblance to the "Simpsons" character.
The Engineering Department Master Chief was no more revered than that. Having never served in Engineering Department, I couldn't even tell you who he was, but I never heard any of the EM or EE dudes referring to a "Bull Nuke."
I think that maybe this "Bull Nuke" is a tuber-term like the Chief of the Boat (COB). I always heard all of my tuber friends from NNPS and NPTU referring to the COB, like they knew him and he had some noticeable effect on their daily lives. Yes, we had a Command Master Chief, but he was usually an Air Dale of some sort and no blueshirt in Reactor Department would've known who he was [by name and/or sight].
MGM