You don't need to take any of the old water. Keep your bio media submerged in conditioned (Seachem Prime or something similar) water and you won't kill off any bb. You don't have to wait any time before introducing the fish back into the tank. Unless of course it's waiting for your heaters to bring water to temp once you've set the tank back up, but you should try to refill with the right temp water so you don't have to wait. With the already established bb you should get an "instant cycle" effect.
Moving period is stressful to fish. Keeping old tank water doesn't help stress them any less.