First thing I would do is remove all the bio-filter media like ceramic rings from the main filter, rinse it aquarium water and dump into the tank. That should save most of the BB on the media.
Depends on what is in the tank. I have been able to keep smaller fish like tetras alive by doing regular small water changes and not feeding to avoid excess waste polluting the water. If the tank is full of (for example) goldfish you would definitely have to add a batterey operated airstone and keep up on water changing at regular intervals until the power comes back.
