There's two kinds of bouncing: a slow bounce that usually happens when you go over curbs and bumps, and a very fast stutter that can happen when driving on inclines and banked corners.
The former is caused by the rear springs being too stiff. There's two solutions: soften the rear springs to around 3.6 or lower, or stiffen the rear dampers to 3 or higher. Personally I find that softening the rear springs works best, as if the rear dampers are too stiff, the car can feel clunky and unresponsive while turning. Sometimes you don't have a choice though, with cars like the R33 V-spec '97, the TRD 3000GT, the Nismo 400R or the NSX Type S's, as their rear springs are very stiff even at lowest settings. With stiff rear springs and dampers, you'll notice that the car will try to bounce, but will stop halfway and return to the ground.
The latter is caused by stiff dampers, usually 6 or higher, but sometimes less depending on the car's weight. In extreme cases, the stutter can halt the car's acceleration as well, noticeable on tracks like Grand Valley. The RPM needle will shake violently while this happens. The solution is to soften both the front and rear dampers to 5 or lower each side. Cars like the Concept Car LM on NTSC-U/-J, the Cerbera LM on NTSC-J, and racing-modified Griffith's need even softer dampers, to 2 or 1 each side.
Depending on the car and track, the stutter can be used to your advantage, as it greatly reduces braking distances and makes the car much easier to turn. It's much more useful in GT2 though, as it can be used on front-heavy, understeery cars like the GT-One road car to help them turn, at the cost of instability over bumps.
Due to fewer physics calculations per second, PAL cars tend to bounce more than on NTSC versions in both GT1 and GT2. Raising the frame rate (by playing the GT Hi-Fi mode, using Silent's high-FPS codes or otherwise) will fix most bouncing and instability issues.