You can make a tremendous dent in the Bullhead by fishing them out. The only thing that stinks is that it's kind of like work to do it.
I just came from my pond, and at our pier where we hand feed, I arrived and the bullies were the first thing that showed up before I even threw feed. I wished I had a shotgun and multiple shells.
So I had another purpose at my pond (transporting some bluegill to stock a neighborhood retention pond), and convinced myself to fish those hundred or so bullhead out. I could have taken 30 per hour. Too lazy, to a degree.
But again, it's just work.