Roads go through a variety of disturbed landscapes that expose the ground below. For instance, some roads are cut through hills and you drive through a channel cut in the rock. Roadwork often plows up ground. There’s also the case that just driving for hundreds of miles will allow someone to see lots and lots of varied landscapes where natural erosion may expose the ground underneath. With all that driving around, have there been cases of someone looking out the window and just happening to notice something in the landscape that turned out to be a dinosaur bone or some kind of fossil like that?
As for driving through channels cut through limestone, if you notice some of the limestone is yellow and crumbly, it may contain fossils of shells. You can’t see them when driving, but if you happen to stop next to some crumbly, yellow limestone, look around and you may find some fossils.
I’d be surprised if that has ever happened. Any fossils would more likely have been noticed by workers building the road. When you are driving you are not likely to spot a fossil as you speed by (they tend to blend in to the environment).
That said, important fossils have certainly been discovered by people just walking around and stumbling over them.
The famous T. rex “Sue” was found by a fossil hunter who, while hiking, just spotted some bones partially visible on the side of a small cliff.
Hendrickson spotted a few large vertebrae jutting out of an eroded bluff and followed her hunch that there were more beneath the surface. In the end, it took six people 17 days to extract the dinosaur’s bones from the ground where SUE was discovered.
< snip >
At more than 40 feet long and 13 feet tall at the hip, SUE is physically the largest Tyrannosaurus rex specimen discovered, out of more than 30 T. rex skeletons that have been found. SUE is also the most complete—around 90 percent. We have 250 of the approximately 380 known bones in the T. rex skeleton, including the furcula (wishbone) and gastralia (a set of rib-like bones stretched across the dinosaur’s belly, believed to have helped SUE breathe). - SOURCE
Not from driving, but walking on the Oregon beaches where there are eroding bluffs reveals tons of shellfish fossils.
Then there was the British woman Mary Anning who started fossil hunting at an early age along the cliffs of the English Channel. She discovered the first ichthyosaur skeleton when she was twelve.
How many non-fossil hunters would even recognize a fossilized bone if they stumbled upon it? Just another funny looking rock.
I wondered about this when writing my post (just above) and I am almost positive I would not have recognized the bones of the T. rex that Hendrickson did. As a fossil hunter she had a better eye for this stuff. I’d need something way more obvious (like a skull) to even begin to think I found something. If I were in Hendrickson’s place that day I have no doubt I would have walked right on by and never given it a second thought.
Likewise with Mary Anning who @Chefguy mentioned (although I do not know the specifics I also suspect I would have walked past oblivious to what she saw).
YMMV
Not quite what the OP had in mind probably but places like the Maysville roadcut in Kentucky are well-known by enthusiasts and professionals as spots where you can pull over and find fossils with relative ease.
You’d need an almost miraculous combination of circumstances to have this happen. It would need to be a road cut through hard rock with no covering vegetation that also is subject to erosion so that a fossil suddenly becomes visible but a fossil so large that with just a bit of it exposed an eye in a moving car could see it and distinguish it as a fossil. Not impossible, but more likely on some two-lane road in Montana or Alberta than on any modern highway, maybe a road that goes to a known fossil field with experienced eyes already primed.