i know it doesn't take 6 months to get a good colony of BB in a sponge. i rinse the sponges out after only 2 weeks in the tank and there is already plenty of biological material in it.
i guess the time would depend on stocking level in the tank, and how many sponge filters are in the tank and if they are the only filtration or not. but the entire nitrification process only takes 6 weeks at the most and if you're just changing a single sponge in an established tank it shouldn't take any time at all.