I've had a pond for 11 years that has not acquired fish. It existed before that, too, but I'm not sure for how long (I think several decades).
It has lots of amphibians and snakes. Rarely any birds.
It has lots of amphibians and snakes. Rarely any birds.
Snakes are active but I doubt they eat nearly as much as the bullfrogs.
Could also introduce fish that will eat the frogs to keep them under control. Or just leave it all as-is.