JB,
When I was a kid (a long time ago), I helped my grandpa set hoop net traps in the Sangamon river in Illinois. He would bait them with small burlap bags filled with cheese bait. We would check them twice a day and they were always loaded with cats, bullheads and carp. I have seen these traps for sale in the Netcraft catalogue. These traps might help you clean out your bullheads and you could throw back your desirable fish.

Brad B.