The terms mudcat and bullhead generally refer to the same family of fish.

I trapped a lot of bullhead in big minnow traps with the holes cut larger. The best bait for bullheads seemed to be dead fish. However I caught the most bullhead in traps baited with bread, that attracted FH, which the bullhead would then gorge on. I also found that traps left overnight usually caught fewer bullhead than those left out for an hour or two. Once the food was gone they must have been able to find a their way out. Chumming or feeding in the area you throw your traps also helps. I think any fish trap will work for bullhead but it will also catch other fish, which, in that confined space, the bullhead will be able to catch and eat.

Another method to consider is a baited hook left out overnight. Bullhead tend to "swallow the hook". I have not tied this but I think it will work and be pretty selective. If you are planning on adding bass in the near future, perhaps the best option is to do nothing. I doubt a few bullhead will cause much problem as long as there is a decent predator population.