*sigh*...I wish my goldfish would stop growing too...
Yes, you can add water from their current tank into the new tank. In fact, transfer over as much as you possibly can minus all the gunk and stuff that is all in the gravel. Transfer any old filter media into the new filter as well, especially sponges or floss. How long the cycle process takes I don't know, I don't think there is any set time period or rule of thumb to follow except for your test kits. Monitor ammonia and nitrites, and when both are reading zero, supposedly the tank is cycled.
Of course, that doesn't work if you have nothing in there to cycle the tank in the first place. The old water definately helps with a jump start, but that is only cycled to the previous volume, so the addition of fresh water could very easily dilute the bacteria and thus bring your biological capacity back down to zero in the larger tank. The Cycle stuff...I don't go by that. For all you know, the stuff in the bottle was sitting on the shelf for so long it's dead.
If you want to do a little fishy cycling, put one of your goldfish in there and monitor your ammonia/nitrites every day. If either appear to be getting toxically high, do small volume water changes (5-10 gallons) frequently (every day to every other day). Personally, I have never had a problem with using fish to cycle a tank provided that a person is on top of what is going on and doing chemistries -every- day. I know everybody here will probably tell you I'm wrong, that fishless cycle is the only way, but goldfish are durible little critters that love frequent large volume water changes anyway, so no matter what, unless you've got good biological filtration (biowheels or sponge or such), you're going to be recycling your tank with almost every water change, so you'll have to stick close to your ammonia kit.
Once ammonia and nitrites are down to zero with one fishy you now have -the biological capacity for =one= fishy-. Do a regular maintance water change, then add fishy number two and repeat the monitoring/water change routine. Do the same with fishy number three. Don't forget to maintain their old home as well.
For full grown 8"-10" fantail goldfish, a 55 gallon tank is considered a good home for only -two- adult fish by breeders and goldfish experts in all the literature I've read. This is because goldfish need more O2, therefore more water. If you plan to keep three...plan on doing more frequent water changes. If you plan on more than three...I would do water changes at least 20 gallons once a week. Right now I've got six three inch fish in a 29gallon tank, and I'm doing five gallon water changes twice a week. The three one inch fish I have in the 20 gallon get six gallons twice a week.
~~Colesea