Well, that depends. The bacteria need oxygen and ammonia to survive. I imagine there'd be enough waste on the filter media in various stages of decomposition to sustain for them a little bit. However, like I said, they need oxygen. The O2 content of your bucket of water is going to depend on the temperature of the water, the amount of surface agitation and the surface area exposed to air. Given that you're probably keeping the bucket in a room that's probably somewhere in the ballpark of 65-70 degrees.......probably no more than a few hours. I'm sure the bacteria are metabolizing the available O2 faster than it can be replaced by dffusion. Plus, the water is stagnant, so there's no opportunity for air to really mingle well with the surface. Put an airstone in the bucket with the filter media and you can buy yourself some more time.
It's not like the bacteria colony is all going to die off completely after a certain time period elapses. Rather, it's going to start shrinking in size as the O2 and ammonia levels drop off. So, even after a few hours pass, you'll probably still have some bacteria left. It just won't be as strong a colony as you started out with. The longer you wait, the fewer you'll have left until, eventually, they all die. I would imagine that that would take a pretty long time.