With a sharp enough knife, skinning is not necessary. Filet just as you would a BG, but I don't cut through the ribs...just around them. Otherwise, skin as above, then filet.
Leave the belly meat (UNLESS it's a flathead...that's the best part on them). Larger fish, I also "filet the filet" and get all pieces roughly the same size/thickness, so they all cook at the same rate. No more than 3/8" or so...
Don't care much for bullheads...but some adore them.
I prefer dry breading (Shore Lunch or Andy's are both great), but to each their own. I also trim off ALL red or yellow meat (mudline and fat) as that's the part that contributes an "off taste". Rinse over and over, until really clean, then refrigerate in water. 10-15 mins before frying, add a couple tablespoons of lemon juice (fresh or Real Lemon)...drain well, bread and fry @ 350F until golden.
CC are not the prettiest fish...but they look great surrounded by hot oil!
I may try to get a short video or several pics next time I clean one of 'em...easy enough to do.