Benching a Mountain Rifle for Groups

I shoot light rifles the same way I do heavier ones. I prefer shooting off Bipods if I can, mostly because my "rests" are usually socks full of rice and not horribly resty.
What I've found, is that when setting up the shooter and rifle NEED to be aligned with the target naturally. That usually insures recoil comes straight back and you don't have the gun jumping all over the place.

If I'm going to hold the gun I'll put the rifle in my left hand, and that hand on the rest. This used to be my go to method for dealing with jumpy rifles, but having shot my .375 Ruger enough to get used to dealing with THAT, I've found that alignment is the cure, and holding on to keep a gun from jumping is mostly just a band-aid.

A hand on the front scope bell is a bad idea. Tubes flex.

Try holding the forearm with your hand. Then rest hand on sand bag.

Don’t forget to shoot it from hunting positions.
My Remington M7 in 7mm08 will shoot low if benched, then shot from normal positions.
I sight it in shooting from a sitting position with my back against a support, simulating sitting against a tree. I don’t hit or miss low anymore...