Short answer: 6 weeks.
BB will start growing on the new media within days, but it will take about six weeks for the BB to be "established", meaning they have both kinds of bacteria (the ones that eat ammonia & the ones that eat nitrite) in large enough numbers that you could remove the older media, if you wanted, and not "uncycle" your tank.
So if you wanted to remove the old media because it's falling apart, or it's not the type you wanted in your filter, etc, or if you wanted to take a piece of media and use it to "insta-cycle" a new tank, I'd wait 6-8 weeks after you've added the new stuff to be sure there's plenty of BB established on all the media.
But remember, you'll only have as much BB as needed to take care of your fish's ammonia output, and not really any extra. So while it's great to add extra media to your filter- you really can't have too much so long as you're not clogging the filter!- you will still have more or less the same "amount" of BB. They'll just be more spread out over multiple pieces of sponge instead of crowed onto one piece. This is because the BB are alive and if there isn't enough ammonia for them to eat, they won't be able to keep growing their population larger but will instead find a steady balance of numbers.