The bouncing is mostly related to the tires. Cold tires, particularly bias-ply’s, take a set overnight, a flat-spot if you will. It's common to all size tires including radials, though not so bad with the radials. Once the tires get up to operating temperature, they flex more, but they will still launch you to the moon, or the underside of the cab given the chance. Sometimes the bouncing wil only be right at a certain speed, but it will still be related to a tire and it needs looking in to.
The cushioned machines help to take the bounce out thorough a complex hydraulic valving system connected to a load cylinder in the hitch or cylinders connected to the drive axle. It works so that the bounce up is over-ridden hydraulically by the weight of the machine coming down. It sorta balances things out and both systems were a wonderful addition to scrapers when they first came out in the 60's.
There is no easy way to take all the bounce out. The tires have to warm up and the only way to do that is to operate the machine. Sometimes you get a tire or two that have inherent balance problems in them, like a section repair or a big chunk of tread missing, or busted ply’s -- a dangerous condition. Also some tires separate and will cause quite a bounce, if they don't just blow out instead. There is some bounce associated with lose hitch components, and also a bit of bounce that is caused by hydraulic hoses expanding with excessive pressure.
The bounce can be harmful to your health, even cause death from a variety of factors. It's nothing to snort off or fight. Best thing to do is get slowed down or stopped as quickly as possible using the brakes or dropping the bowl very close to the ground. Either way it's rough and hard on the operator.
Overhung scrapers may be a bit worse than six-wheelers, but not by much as my experience has indicated. Bigger tires like 39.5X39's also are a bit better than those on smaller machines with choppy little bumps in the haul road. Bigger bumps and soft spots are bad no matter what you run over them with.
I can remember long strings of scrapers heading out early on cool mornings, some going like hell and some taking it easy. You can figure who was driving like cowboys and who wasn't. There comes a time when operating a scraper just isn't comfortable for older operators, not if they are working a production job. Landscaping or smaller jobs with short hauls is usually different. I dearly love scrapers, but can no longer operate them as I used to. Maybe some of the small tow-behinds, if they are on short hauls.