Home depot sells 5 gallon buckets for $2, $1 seal-rite lid. When you move, fill the bucket with the water. It will help in the new tank, even if the BB is minimal, it still helps, and we're only talking water from a 5 gallon tank.
I have moved so many times, and each time i just fill those orange HD buckets with enough old water to fill 50% of the tanks at the next location, and it's always helped keep things normal. Especially if your new location's water is even the slightness different from your old water, there is the mineral difference, and other things, and the older tank water mixed with the new wont stress the fish out, as much as different water, from a different source. Your conditioning the fish for the change which will take place with water changes as the old water goes out, new water goes in.
You ever go somewhere hours from home, or far far away for a few days, and get the farts haha. It's usually the water, and the minerals, and dissolved organics in it. Even the human body has to change to different tap water from different places