A fast google search gave me answers ranging from instantly to 45 minutes to 5 hours to overnight. Is there no single answer based on actual research? Or is it just because it's what everyone says?
The reason there is no clear answer is because no situation is exactly the same. The bacteria in question consume oxygen, and the more prolific the colony is in a bio-filter, the faster they will consume the limited amount of oxygen available. How much oxygen is still available to get to the bacteria depends on the bio-filter design itself. This is where a shower type bio-filter with it's media exposed to the open air would have an advantage over bio-filters where the media is completely submerged, providing the shower filter media didn't completely dry up. In any case, any of this bacteria sealed in an airtight container (or bottle) would certainly fair the worst.
Whether these oxygen dependent bacteria all die or just go dormant is another question that I don't have a clear answer to myself, but it doesn't really mater in regard to the bottled bacteria question, because if they do die, then the bacteria in the bottle will definitely all be dead, but if they just go dormant (which I believe is closer to the truth), then that would mean the need for adding a few dormant bacteria in a bottle would be totally unnecessary since these bacteria are so prolific they are basically everywhere all the time in a dormant state waiting for just the right conditions to re-activate and come back to life and start doing their thing. Thus again exposing the lack of need for a few more dormant bacteria in a bottle.
An experiment that I already mentioned that you can do at home supports the dormant bacteria hypothesis. Take some of your active mature bio-media and put it in a sealed (air tight) bag or container, smell it and remember what it smells like. It should have a fresh, clean, light fishy smell. This is what a good aerobic (oxygen loving) bacteria colony smells like. Now leave it in that sealed bag or container for 24-48 hours at room temp, then open the bag and take another whiff. What do you smell? It should smell awful. It will have that septic smell, H2S, and methane. This is the smell that
anaerobic bacteria (the kind of bacteria that thrive and reproduce in the absence of oxygen) produce.
So the question comes up, where did these
anaerobic bacteria come from? Certainly not from a magic bottle!