The squeezing of filter sponges into water to then "seed" a tank is often mentioned but I am not certain it has much benefit. Bacteria (the nitrifiers) do not live in water but on surfaces, and they adhere quite well. Personally I do not think you could remove many just rinsing/squeezing out filter foam or sponges. The brown gunk that comes out are organics, not bacteria, and you really do not want this in the new tank.
Using the media itself from an established tank in the new tank will seed it faster. I'm not saying the squeezing will not, I just question how much. I rinse my sponge filters under the tap every week, very, very thoroughly; I don't know how much bacteria is still adhering, but from what the experts have told me I suspect a fair number. The chlorine does not kill them either, again depending upon the specifics (chloramine in the water is much stronger).
You asked about the bottled bacteria...these are in a sort of hibernation stage, and they can live like this for some time depending upon circumstances. They can go into a similar suspended state in an aquarium filter too.