Most of the bacteria hang out in the filter and gravel of the tank, I guess there are some in the water too, but you can only really look at that as a 'seed' for the filters in your new tank.
Best option is to run the new filter in an established tank for a week or so and let it pick up a usefull bacteria load. That will definately cut down the cycling time. Thats what I do with a new tank, then a few crash test dummy guppies for a couple of weeks.
Either way, it will be OK to add a FEW fish to your new tank and monitor conditions as it cycles. The nitrate cycle wont establish properly untill you get some bio-load going into the tank. So the water is probably perfect right now, it's that first couple of weeks of feeding fish in there that is critical.
Like Mr P says, take it slow, a few fish at first, build up the numbers over a few weeks and you will be fine.
Cheers
Ian