Gee... Im really not sure if a three hour drive is good for a fish or not. Especially the bettas who are air breathers. With a bag closed up for that long they can run out of air. I was in the same position yesterday when I traveled 3 hours away to visit my daughter for the day. I really wanted to stop at a huge aquarium store they had there in town, but my husband talked me out of it. He really thought that the three hour trip would not be good for the fish.
I hope someone out there lets you know.. and then I will also know if its ok to keep fish in a bag that long a trip!
IMO If you had the ability to get the fish without having to drive the three hour trip, then that would really be the best route to take.

~ kate