Jody,
In my experience and I've transported a lot of flowers your always going to have some water accident. So if you drive a nice van get one of those rubber trays they make for the back of vans so it will catch the water. Now then, I have not had too much problem with 5 gallon buckets tipping if they don't have too much water in them and just enough to make them sturdy. I prefer the 2 1/2 gallon buckets because they don't smash my flowers as much. If your basement is cool then there would be no need to refrigerate. Most flowers can survive one night in a cool basement and be just fine the next day. Are you using plastic sleeves for the bouquets? If you want to prevent as much damage to your flowers in transport it might be a good idea.
Best of luck,
Kathy