In a cup of water is not an option?

Mint do root quickly. Depending on how far off the move is, you may be able to pot it up before moving.

If not, how about putting it in a ziplock baggie with a tiny bit of water. Make sure the baggie has a lot of air in it and seal it up. The extra air makes a bit of a balloon to cushion the plant. Try not to keep it sealed up for more than a day. Get it back to rooting in a lighted location with fresh air as soon as you can.

FataMorgana