Two things that helped me to spin at 120 plus:

When I first started training higher rpm, I would tighten up my core muscles when a bounce first started. This would push off the bouncing for another 20 rpm or so. I would think about drawing my navel to my spine.

Second, I am naturally a heel down pedaller. At higher rpm, I would become a heel up pedaller, which would effectively lower my seat height. I never knew this until I had a video made of me pedaling. Once I figured that out, it helped smooth out any bounce.