What kind of bullheads? Bullheads are awesome catfish. But they can be bullies. Pretty much anything alive in the aquarium (fingers included) that touches the barbels will get bitten. Combine this with the fact that sunfish sleep when bullheads are most active. Perhaps if you raise them up together they will get along? Or if you have a few to diffuse aggression?
When I was 16 I caught 2 baby, 1.5 inch, bullheads out of a golf course pond in the middle of January. I put them in an aquarium together, and I thought it was the coolest thing ever, neat little catfishes they were. They did fine for about a year. But then the dominant one started eating all the food. I noticed that the dominant glutton started getting tattered fins, turns out the beta was picking on the alpha. It all ended in one big fight, in which they both got beat up pretty good. I separated them, and still have the bigger, going strong. Tried putting a sunfish in there, ended up becoming a chew toy. They seem to display some sort of territorial behavior. Good luck!
