I don't do a lot of shooting from the bench. Normally I shoot from the bench only to establish an initial zero, which I will then confirm from a more practical field position, like prone with brace sling or over my pack. My rifles are meant to be carried in the field and used from a variety of positions. I don't have any heavy, purpose built long range/accuracy rig right now. In fact, I mostly do about everything with my AR-15. With these types of rifles, I try to mimic field positions, so I will have control of the forend over the bag up front with my support hand, applying pressure to the rear with the angled foregrip (or with a traditional bolt action, with the front sling swivel), intentionally pretty much identical to how I would shoot the gun over an improvised rest in the field.
Most purpose built long range/accuracy rigs are built heavy. Weight adds inertia, which makes the rifle for stable, and adding metal and material to barrels, receivers, stocks, ect makes them stiffer and more rigid. On the rare occasions I shoot one of these rigs, like my brother's AR-50, back before he sold it, I would adopt the more traditional benchrest position, allowing forend to either sit neutrally on bag or rest, or with slight tension leaning into a bipod, and then using my support hand back at the shoulder to make minor adjustments and keep the rifle welded to my body. The trick is to get your position set up so that you're not wrestling the rifle. The point of aim should be natural. If you have to muscle the rifle to keep it steady, then you need to adjust your body, your rest, or both. The point of shooting from the bench is to remove as much human error as possible. This still requires the human to be patient and proficient. Trying to muscle a rifle into place in order to rush a shot is how groups open up.
Shooting a rifle under muscle tension is more like shooting from field positions and improvised rests, and in my experience does best with a more aggressive stance. I like to get a clamp grip as far out on the forend as possible so I can really drive my muzzle, but I am six and a half feet tall, so your results may vary.