Don't forget that the gravel/substrate also houses beneficial bacteria I would move this over as well, as others have stated moving the old water is not necessary. However if you don't do water changes often and by often I mean at least once a month I would keep about half the water so to not Shock the fish since the nitrate will drop drastically
Hello; There are two ways I use substrate (gravel in my case) in a new setup. First is just to "seed" a new tank with bb colonies. For this I give a hand full or two of the gravel a light rinse in old tank water to remove the detritus and find some way to suspend it in the new setup. That way I can remove it later for a good cleaning.
The other way is to give the old dirty gravel a thorough rinsing before placing it in the new setup. To me putting old dirty gravel into a new setup starts the new tank out with a heavy load of detritus (mulm, fish poo, decayed food bits and all).
I use two or three five gallon buckets that are only used with my tanks. I get a stick to stir the gravel with, usually an old broom handle. I use a garden hose with a nozzle set to a jet of water. I clean about a half gallon to a gallon of gravel at a time.
Put the amount of gravel into a bucket you can handle and hit it with a jet of water and then stir it up with the stick. Pour off the dirty water while it is still stirred up. Repeat until the stirred gravel is fairly clean and dump the cleaned gravel into a clean bucket.
I get that some of the bb are rinsed away as well, maybe most of it. I also get that the tap water with chlorine and/or chloramine may kill off some of the bb. I suspect that at least a few of the bb will survive in the wet gravel but the purpose is to "clean" the substrate. If you have never cleaned old tank gravel/sand the amount of detritus that can be in it may be a surprise.
I get the bb colonies for as new setup several ways. As mentioned on filter parts. Also on most any other solid surfaces that can be moved from an established tank. On snails and maybe on live plants.
I also like to keep extra sponge filters or few going in tanks for quick set up. The sponge of a sponge filter can be spilt into two parts and a half can be put into a new set up. I also throw the sponge part of such filters in the back of my HOB and let them stay there to be grabbed when I need a quick setup.
good luck