Both of mine are on carpet. I have no where else to put them right now. My #2 Singer 66 treadle is sitting on the little rubber cushions you put under furniture. Raises it up about 3/4". That does help some.
Getting the rhythm to treadle smoothly will help with the bouncing. Also check the grub screws under the machine head that tighten onto the hinges, and check the hinge screws into the wood.
Make sure the ball bearings on the crank at the top of the pitman shaft are well lubed. The crank pivot too.
Lots of things to check and considering the treadle base has no bearings other than the crank lubrication is paramount.
Joe