I would set a rule that every bullhead caught from either pond is removed, whether eaten or thrown on the shore.

Having the ponds 'connected' to streams can continue to create populations of 'new' bullheads, but depending on the make-up of your bass populations, you may see those 'new' bullies getting eaten as the existing 'in-pond' population of bullies gets reduced by culling.

Excerpt from Robert Crais' "The Monkey's Raincoat:"
"She took another microscopic bite of her sandwich, then pushed it away. Maybe she absorbed nutrients from her surroundings."