My Sunset actually really enjoys car rides. Sometimes he sits up high and watches everything go by. Other times he basks on the dashboard, or sits on my knee and chills out. Pretty much anytime I have to leave the house when the sun is out I take Sunny with me. I have not yet taken Pele in the car because she's only been with me a couple of days, but once she has settled in more I plan to take her out to see how she likes it. Errands and day trips are a big part of my experience with my dragons. When I was a child, I had a beardie, and I took that lizard EVERYWHERE. Including school. On a daily basis. Yes, I got away with this. XD She was very quiet and well behaved, Oribeth was. I miss her still. I don't even remember what happened to her. I think she must have been rehomed when we had to move from Santa Cruz to Vacaville, as we rehomed a LOT of our pets then (something we now THOROUGHLY regret -- in retrospect, the very fact that this jerk made us do that should've been a sign that my mom shouldn't have married him, but, you know, hindsight, all that.)
But anyway, the point is, beardies are hardy creatures. They're not going to fall apart just from a simple car ride. Just don't leave it in a parked car alone. As with any pet this is a VERY bad idea.