I have driven both my bettas across state lines several times (out of state grad student) so the drives have been about 4+ hours. I have two small critter keepers that act as their "transport tanks" for the drives.
Start out by putting a towel down on your seat that you will be putting them on (others sometimes recommend putting them on the floor, but then you can't seatbelt them in) which will keep water from getting everywhere.
I only fill the tanks to maybe half way; def no more than half, as water will splash. (i have bucketed seats, so the water level tilts in my car) and put both my bettas in each tank with a VERY soft plant for hiding in.
Once they are in their tanks, I put both tanks side my side in my front seat, half cover their tops with a towel for insulation, air, and padding, and then seatbelt them in.
I've gotten pretty good with regulating heat in my car, so I know when my car is to hot or to cold for them. I've never seen my tanks temp dip below 70 no matter the outside temp/weather when I don't have heat/AC on blasting.
After the drive, they are the first thing to come out of my car, and I put them somewhere warm and dim so they can relax and acclimate.
I've never had an issues driving with my bettas outside a little splashing water. Good luck!