The usual way to transport fish is in a bag with plenty of air. Double bag if there is any risk of leakage, and a bit of tape on the corners prevents fish getting stuck in bag corners.
Air is more important than the amount of water in a small enclosed volume. They'll do fine in a bag with enough air over their water. Air pumps are great for pumping in air, don't use your own breath, it's lost too much oxygen by the time you're done with it. Blow up the bag like a balloon, twist the top tight and fasten snugly with rubber bands.
75% air to 25% water, and the water only needs to be deep enough that it can cover the fish well when the bag is lying on it's side. If it's cold out, place in an insulated container for transport.
Then float the bag to equalize temps in the new tank. Poke a few holes in the bag and allow the new water to mingle with the bag water for about twenty minutes, then let them go. Should be fine and dandy.
edit.. just fyi, people take fish to shows all the time, and they spend up to 24 hours or more in bags or very small containers. So long as there is air to allow for gas exchange, you're good. The other thing is that if they will be in the bag more than an hour or two, you should not feed them for a day before you bag them, so they won't poop, which adds ammonia, which you don't want. One or even two days of not eating does no harm.