For long distances we've found a well-secured kennel in the PU bed to be most comfortable for the dog.
That said:
When I have to carry a dog in the PU bed outside an enclosure, I always make sure that he's tied so that he can't fall/jump out. Just enough room on the lead to allow him to lie down in/near the center forward of the bed. This lesson learned way back when I was a kid:
We were heading for camp with a dog tied in the back- and a look in the rearview revealed the dog hangin' over the side of the bed, dangling there by his neck while we were goin' down the highway!
Thankfully he survived...and I learned a lesson that I never forgot.