One of the ways you can help jump start the cycling of the new tank is to add the filter you will have in the new tank to the old tank NOW and start letting the new filter build up a supply of bacteria before being moved to the new tank. If you do this, you likely need a minimum of one week to allow any bacteria to build up in the new filter, and the longer you keep it in the old tank the better. Then when you are ready to move to the new tank, take BOTH the old and new filter to the new tank. Leave the old filter in the new tank for at least two weeks, a month would be even better, before removing it to insure your new filter has had plenty of time to build up a bacteria colony.
And as others have said, the WATER in your tank does NOT contain much of this bacteria that you need. The greatest concentration of the bacteria is going to be INSIDE the media in your filter. There will be some additional bacteria on the surface of things in the tank (glass, substrait, decorations). But that's just supplimental bacteria. The bulk of it is in the filter.
Additionally, the reason for doing a PWC is to remove the buildup of nitrate in the tank. It doesn't make much sence to start a NEW tank with water that is old that you were going to throw away. That is sort of like moving to a new house, and the 1st thing you take is all the trash cans... still FULL.
Again, because the bulk of the bacteria you want from cycling a tank is in the filter, it would be better to get two filters going in the old tank, start a second tank with "new" water, then in a single day, move both filters and all the fish to the new tank. Any plants, decorations, and substrait you can move will help a little bit. But even if you don't move anything but the filters, you will likely have nothing more than a mini-cycle in the new tank. Basically, watch the ammonia and nitrite levels in the new tank, do a PWC when ever you see the levels above zero, and within two weeks I bet you don't have to do any more PWC to keep the ammonia and nitrite levels at zero. Of course this assumes you don't add any bio-load to the tank (i.e. no new fish until the new tank is established). From there, the only things to worry about is the fact that things like the temperature and pH of the new tank may not be the same as the old tank. To deal with that, you have two choices. One is to simply acclimate the fish to the new tank as you move them the same way you do when you bring a new fish home... float them in a bag to equalize the temp, then drip water into the bag with 'new' tank water to give the fish time to adapt to the new water. The second option that would be more tricky, but would result in no need to acclimate the fish, is to somehow connect the two fish tanks together. Basically set up some system where the water circulates through BOTH tanks.