Rangersedge - I know you've been fighting with the bullheads for a while.
Don't confuse the hollow log/milk can/trash can spawning of catfishes (such as channel catfish) with the spawning behavior of the bullies. The bullies actually build a nest much like a crappie or a bass. They are not hollow-spawners.
I think your best bet is one of the traps that have already been mentioned. Usually, bullies net very well after ice-out and before the vegetation starts growing.
I can't tell you about permits, as that varies from state to state. You'll have to check with the IL Dept of Conservation to see if netting is legal on private waters in IL.
I wrote a short article on largemouth bass control of bullheads. I think Bob might be planning to run it in the next issue of Pond Boss.
Good luck,
Dave