DrD, there are several people that posted with the same problem this spring - including me.
They will compete for food with your other fish.
You can get info on their biology on many websites, such as here:
http://www.tpwd.state.tx.us/fish/infish/species/catfish/ so I won't go into that.
You can make the biggest dent in their population when you first see the black schools of bullheads in the spring. At first they are dumb and they slowly move around the pond. If you have a small boat and seine, you can get most of them out (if you have relatively small pond). With time they get smarter and they move away or deeper, when you try to get close. Individuals start leaving the group about the same time. Bass will make a big dint, but I suspect that quite a few still make it. They do seem to be greedy and bite before my chanells and blues on worms on the bottom. I need to introduce LMB and give it a few years to see if they can keep them in check.