When I bought my truck, it had been sitting in field for two years. You can read more about that here: About the Chevy K2500. Sitting for that long in one spot is not good for tires. I knew I needed to replace them but I didn’t realize how they would affect the ride of the truck as it went down the road. They held air, so they should be fine for a bit, right?
With those tires (pictured above), the truck would have a pronounced bounce at 45 mph and 65 mph. It would be relatively smooth at other speeds. So I thought something might be wrong with the rear axle or something. I finally got around to getting new tires and the bounce went away completely. The ride is now buttery smooth on pavement.
So if your vehicle is bouncing at certain speeds, check your tires. It might be time for new ones. I got some like these (245/75/R16, the stock size for this truck) and they have been great.