I'm all for a rear bag, use one myself all the time. But I never shoot any of my rifles holding the rear bag or "cross armed". I'm always holding the fore end. There's too much chance for bounce, wether it's off of a bipod or a bag. Use a sling too if you've got one, even if using a bipod. Cuts down on fliers big time.
A lot of shooters don’t realise this fact, a bipod can bounce DURING recoil, the movement is very slight, but does happen. Also, if you are twisting the rifle on the bipod legs unevenly between shots, horizontal stringing can be induced. Not all bipods are square to the bore either.
When using a bipod, if a previous known load suddenly strings for no apparent reason, try shooting with the trigger hand ONLY touching the stock with most pressure from your pinky with less pressure going up through to your middle finger. The non shooting hand can be used like a fist under the pistol grip, if no bag is used, and adjusted by squeezing your fist harder or looser, to adjust the sights. Sort of cupping the pistol grip tends to work best.
I rarely grip the forend while shooting off a bench, regardless if I’m shooting off a benchrest/bipod/bags.
I like minimal pressure when shooting, not quite free recoil, but not a death grip either. A good cheek weld is not difficult to get using a one handed grip. I often practice on the kitchen table dry firing and watching if ANY of the sight picture changes after firing pin fall.
If the boarder of the scope picture even changes position in relation to your eye, then your cheek weld is not firm enough.