We’ve been sleeping on a platform bed for about 15 years now - a firm mattress with no box spring, on a hard base. The lack of a box spring is, I think, critical to minimizing bouncing around when your sleeping buddy is restless.
In the last 3 or 4 years we’ve supplemented the mattress with a 3" memory foam mattress topper. It has ben a god send for me, because I have shoulder problems and no matter how much I try I can’t stop rolling onto my side while I am asleep. With the memory foam pad I no longer wake up with painful shoulders.
An actual memory foam mattress might be the way you want to go, but if you can do a firm mattress (or even your current mattress) and a platform bed instead of a box spring, that would be less expensive and will go a long way toward minimizing movement.