I've taken quite a few long (10 hours plus) road trips with my budgies. The only thing that bothered them was driving at night. I had to keep a light on in the van (we call it a "budgie hauler") so they didn't get panicked by the oncoming headlights and jolts as we hit bumps. Surprisingly, even though the ride was rough (an old van amplifies every road bump) they never fell off their perches. Many of our road trips were around Christmas and the days were short making it impossible to avoid any night driving. You have to keep temperature control in mind when traveling with birds. Heat up the vehicle before loading your birds into it and use the AC if you're traveling during the summer months. And don't leave your birds unattended in a parking vehicle when there is any risk of them overheating or getting chilled.
During one of our road trips several years ago, one of our females and her cagemate boyfriend decided to start a family when we were 16 hours from home in January. They had a nest box but had never laid eggs until then. We had to return home while she was two weeks into brooding a clutch of six fertile eggs. I tried to put soft nesting material in her box to cushion her eggs but she threw it all out. She sat tight on her eggs for the while bumpy road trip home but the rough ride scrambled her developing eggs and none hatched. Two weeks after I removed the dead eggs she began to lay another clutch. It was too soon (not enough rest between clutches) and she became egg bound after the third egg and died. I couldn't get her to a vet because it was midnight on a Saturday and no emergency vets in Maine saw birds. It was horrible to watch her die like that. I tried a steam bath and olive oiled her vent but nothing helped. I didn't have any liquid calcium (Calcivet) to give her. This tragedy could have been avoided if I had removed her nest box before the road trip so I do blame myself. Back then I didn't know as much about breeding budgies as I do now.
Overall, my budgies handle road trips very well. They even seem to enjoy them. They seemed to like to looking out the windows. They travel in their full sized cages (24x20x24) which are a hassle to carry in and out of the van but they need them when we are away for weeks. Each of the four cages of budgies (two in each) gets a big fat millet spray to keep them busy and happy. I removed their water bowls while driving because the water splashes making a huge mess. Make sure you have a flashlight if you're going to be driving in the dark. I also bring a portable vacuum cleaner for any messes they create along the way and bottles of our great well water from home so they don't have to drink strange tasting chlorinated city water while away from home.
Bon Voyage!