Hi there!
I have to drive my buns 7 hours to get to my parents place, and they recommend letting them romp every 3 hours, however I let them romp every 1.5 hours… I got my buns used to putting on a harness, and would stop and let them out on the grass for a bit, and give them some water (although they never actually want water). Before I got the harness’s, I would let them out in the car to stretch their legs and such for a bit. They mostly relax in the car though. When I get to my destination the first thing I do is set up their cages and put water in it, because they are thirsty, and although they lied down in the car, they didn’t really relax, so they enjoy time to sit comfortably in their cages for a bit getting used to new smells, and then letting them out to romp after that.
Just wondering about the travel conditions for your bun? I’ve done lots of research on this (as I have to travel with mine often), and have come to the conclusion that no matter how much you want to give them to be comfortable and move freely, it is safest to have them in a small travel cage (large enough to lay long and sit up tall, but not really move around), as if you were in an accident, there wouldn’t be any room for the bun to get thrown against a wall, or another object (they just get pushed into it), so they are less likely to get hurt. I put a hefty amount of “fluff” (litter fluff.. uhm. Recycled paper bits) in the bottom, its stuffed animal, hay, and some treats. (They will eat the hay, but they won’t eat treats or water usually while in the car).
I also check the temperature where they are quite often, and adjust as needed.
I hope this helps. Good luck with your move!