Nothing wrong with not wanting to drop a pile of cash. I know the feeling...

I'd go with the aeration, it will help improve the water quality and will hopefully help the bass stay alive in the pond. I would catch as many bullheads by hook and line as you can. Bullheads actually are pretty good eating IMO, but they probably make great fertilizer as well.

Also consider buying a couple fish traps. They're not very expensive and the kids will love checking them in the mornings after a night in the pond. Bait them with livers or something else stinky and you'll end up with plenty of bullheads.

Hopefully with the aeration and reduction in bullhead numbers the water quality will improve enough that your 12 or so LMB that you catch and transfer to your pond will survive and help control the bullheads and sunfish even further. I doubt the bass will affect the bullfrog numbers that much.