You can control most of the bipod jump if you "front load" the bipod, that is press it forward with your shoulder to put some forward pressure on the bipod feet. That seems to cause the rifle to recoil straigt back instead of hopping up.
I find that it really helps get repeatable recoil.
The F-Class rest that I also use eliminates the bipod bounce entirely, partly because the feet are actually arcs instead of rubber feet. It is clearly more stable and more repeatable, but you can't always use an F-class bipod, but you almost always can had a collapsable bipod ready.
An adjustable front rest allows the rifle to recoil straight back.
The benchresters set up the adjustable front rest with a front bag that matches the rifle foreend and use good solid rear bag that lets the rifle slide back freely. They only touch the trigger so the rifle "free recoils' straight back. That is how stable that configuration can be.