Just keep the bio media in tank water or treated water. The only problem you would have is if it dries out.
Hello; I have not transported bb loaded media for 12 hours only 10 hours or so, so my response will be a guess to some degree. I have kept filter parts and media in buckets for a day or so.
Keep it wet is likely the key.
The beneficial bacteria (bb) are sessile. By that it is my understanding they form colonies on surfaces as a bio-film. This film is reported to be fairly sticky which to me means it stays on those surfaces fairly well.
You have not defined the type of media so I will speculate a bit. The filter bodies and the tubes which move the water around are, to me , prime real estate for bb colonization. I would give such things as the tubes a gentle rinse in tank water to remove any loose gunk and put the tubes in a container of tank water. I suspect the bb bio-film will be largely intact.
Another guess being that while some of the bb may be lost and some may die, is that most will be viable.
Other surfaces in a tank should have bb on them. I would take such soft things as floss or sponge filters and give them a few squeezes in a bucket of tank water to remove the loose stuff and then put them in a container of tank water for transport.
Other solid media such as bio balls be given a simple rinse and again kept wet for transport.
Not sure you need to carry much water. I never have taken more than what is needed for bagging my fish. Good luck