On paper, you'd need a collector license. In practice, the government wouldn't care about one bullhead, I reckon
Bullhead can be a gamble. It's a scavenger but it has the equipment to swallow large items. Bichirs are of easy to swallow shape but you'd have to hear from a bichir keeper, as I am not one of them.
Bowfin is too a gamble. They are voracious feeders without overstatement.
IMHO you could try but I'd watch them like a hawk for a long time and I'd need to have the means to separate offender(s).
What requirement are you asking about?
Of bullheads, there are many species, about half a dozen or more. You gotta know which one you will be dealing with.