We tried this experiment 2 years ago by purchasing 3 aquacultured Bhergia Verrucicornis (actually, they're Aeolidella Stephanieae, but
anyway, the white fluffy aeolids who eat aiptasia). So we kept them
in a separate tank until they bred up to about 100 offspring before
releasing them into our then infested 55 gal tank. Took 'em about 6 weeks to clear the infestation. We then had to scramble to find homes
for most of them. We tried keeping a separate tank for breeding aiptasia for food but it's a very tricky process. This is a struggle against population dynamics - who's going to reproduce faster, the nudibranchs or the aiptasia. In theory you could make it work if you have a LOT of aiptasia set aside in another tank. But it's alot of work. This is an easier problem to solve with a small tank. Big tanks make it hard to find all the pests and predators.
If you only have a few rocks infested, I'd consider removing them from your main tank - put them in a smaller holding tank and introduce the berhies into them unti they eat all the aiptasia. Then give the berghies to new homes and don't return the original live rock to the main tank for several weeks (make sure no aiptasia survived....they're really hard to kill). Best of luck!