how long does it take for bacteria to eat ammonia?

If ammonia is off the charts you need to change water.

High ammonia can harm the nitrite eating bacteria.

Get those fish some good fresh water before you damage them, then take some more sponge or filter gunk from the big tank and put it into the filter for the little tank. I wouldn't put the whole thing in, just squeeze it well and return the sponge to the home tank.

Keep measuring the ammonia and nitrites, change water and add filter squeezings if necessary.

Not good to let the ammonia get ahead of you, change a lot of water, maybe several 50% in a row to get ammonia down to not readable.

There is no way to predict the time required without knowing the numbers of the two nitrification bacteria - which is no easy task.

But when the colonies are mature, the ammonia and nitrite never come anywhere near detectable levels, the stuff is effectively oxidized just as fast a it is generated. But the bad news is that their doubling time is quite slow, for bacteria.

Keep changing water!

I had to do 3 water changes back to back when I was cycling my first tropical tank... each WC was 50 to 85%, it was bad, really bad, I back calculated that the nitrites must have been at about 15 ppm.

I was changing water twice a day for the next couple of days. (I had killed the filter bacteria with bleach then didn't scrub the dead stuff out well -- ammonia factory!) Keep testing, twice a day, change water asmany times as it takes to get the numbers down to something reasonable, like 1.0 ppm or less.

Are you using something to sequester the ammonia to protect the fish? Prime or something similar will bind the ammonia and nitrite so it won't harm the fish, but let the filter bacteria use it properly.