If you’re bouncing, it’s recoil management. I went through this as well. In my opinion it’s part shooter and part chassis/stock design and adjustments.
Also I’m not a fan of bench shooting no matter what they’re made of.
But if you’re married to some bench, why not go all in and get the whole bench setup?
If you’re wanting the ability/option to shoot in a realistic practical environment, which is what the bipod indicates, where you are a larger part of the equation, then shoot like that all the time. Prone, bipod, bag.
Bipods on benches, in my opinion, are not ideal. If you master it, it’s doable. Train how you intend to shoot. I see hunters on sight in day shooting off benches and think it’s counterproductive.