I sometimes take my chams to the park, when i drive i don't box them up, IMO thats more stressful than holding them (if theyre chill with you) or putting them on a plant. I have put them on a plant and held it. It was a bit bumpy, but nothing as near as swingy and bumpy and a chameleon on a branch on a windy day.
If youre the only one in the car its different.