Just take a few sponges out of cycled tank filters and rinse them out in the new tank. Then add ammonia as if you were doing a fishless cycle. You should have the new tank cycled for fish anywhere from almost immediately to a as long as a week.
You may need to add ammonia again. Just test and see when it is cycled. The advantage to doing things this way as you do not remove too much bacteria from any one tank. This is similar to using a decent bottles bacteria but a bit messier.
When I had to set up and run my bio-farm to cycle enough filters to be able to drop them into multiple new tanks and then add fish right away I did the above, But I also would get a smaller bottle of Dr, Tim's and added that as well, But I was cycling filters for as many as 8 tanks holding a total of over 200 gallons. I needed to have those filters co well colonized that I could fully stock the new tanks. Because I did not set all the tanks up and stock them in a singled day, it was easier to keep the remaining filters cycled in the bio-farm until they too went into tanks. It was a lot easier to cycle all the filters in one tank than to cycle 8 tanks separately. It took me 10-14 days to get all the filters full cycled from scratch.
The reason seeding a tank with the right bacteria is that the full cycle goes very fast because both the ammonia and nitrite bacteria are present from the start and in the right proportion. Whatever amount of ammonia the filters can turn to nitrite, there are also enough nitrite bacteria to handle it. And even if all one can start with is only 1/2 of what is needed, the bacteria will reproduce in response to the ammonia dosing. The bacteria will for sure double in number in a matter of days.
In my bio-farm I started with less seeding than I would have done were it only a single tank. I could have made things go faster if I wanted to buy more of the Dr.Tim's. But, ammonium chloride is cheaper than the bacteria and I was willing to spend a little time getting it to reproduce. Te good thing about having both types of bacteria at the start is I only tested for ammonia and TDS. I needed to test the TDS to know that there was enough carbonates and bicarbonates in the water for the bacteria who use inorganic carbon.
In the bio-farm those two things can get used up fast. I always have to run one or two bags of crushed coral. Since those things contribute to TDS and can be used up fast, I knew that the change in TDS would be due to a drop in the carbonates moreso than anything else contributing to TDS.
Also, as noted above when the bacteria sense the lack of the essentials then need, they will go dormant. When what they need returns they wake up and get back to work fairly fast. How fast is a function of what condition they are in when the go dormant. The better this is the faster they can recover.
What will cause the bacteria to die off is if one has no fish or other ammonia source and we must add ammonia. of we add too little or add it with too much time between doses, this will cause the bacteria to reproduce mor slowly and the the numbers will shrink. The individual cells live for about a day. Whether or not they will divide depends on the ammonia levels. More ammonia and more of them reproduce and faster.If the ammonia level is decreased, then so to will the size of the bacteria colony.
We can actually control both the amount of bacteria in a tank as well as where it might be living. In my pleco tanks which use Mattenfilters and cubefilters made with Poret foam I want as much of the bacteria in the foam as I can have there. To help this happen I tend to deep vacuum the 1 inch sand bottom right down to the bottom glass regularly. If I remove some of the bacteria from the sand, it means there will be more ammonia in the water short term. The bacteria in the foam sensing this will reproduce faster. And the result is there will soon be enough bacteria overall, but it will have increased in the foam more than in the substrate.
However, the bacteria will always do best where the circulation is best. Everything they need must be delivered to them which is why in tanks, much of the bacteria will be in the filter media. To thrive they ammonia or nitrite, oxygen, inorganic carbon and a trace amount of iron. What is interesting in all of this is that the recently discovered ammonia oxidizing Archaea use copper rather than iron to do their thing. Both the iron and copper are oly needed in trace amounts but are essential for the two microorganisms to survive and thrive.