It's been my observations that the single most common cause of horizontal shot stringing when rifles are rested atop something on a bench top is how the rifle's held when its shot. The angle between the rifle and a line between the shooter's shoulders is often not exactly the same for each shot. Which means the muzzle will point to a different place horizontally when the bullet exits. The rifle's bore axis moves a little before the bullet leaves the muzzle.
There's another cause that compounds the problem; trigger finger's not pulled straight back each time and the impact of it coming to a stop an an angle to the bore axis moves the rifle a tiny bit sideways before the round fires. Heavier trigger pull weights compound this problem.
Dry fire your benched rifle noting carefully which way the scope's reticule jumps when the firing pin slams home. If it moves any amount in any direction, you're moving the rifle off the desired point of aim before a bullet will leave the barrel when using live ammo. You'll have to keep your aiming eye open to see this happen. Learn to keep it open when firing live ammo, too. Have a friend load (or not load) your rifle where you can't see that, hand it to you then you shoot it. If it jumps a lot when the firing pin falls on an empty chamber, you're flinching and that really changes the direction the bullet leaves at; it won't be where you want it to.
I had both problems when I first started shooting for accuracy in competition. Some of the masters convinced me to quit shooting a hand held rifle holding it atop a bench and switch to a good prone position laying on the ground. That worked much better. Horizontal shot stringing stopped as my position and rifle hold was more repeatable from shot to shot.
Most interesting was when I went back to shooting a hand held rifle from a bench, shots went about 1 to 1.5 MOA to the right from zeros established shooting prone. When a couple of southpawed shooters I shot with said their benched groups went to the left from prone zeros, that turned on a light in my mind.
No wonder most benchresters shoot their rifles in virtual free recoil. They only touch their few-ounce triggers after shifting the rifle to put the sights on target where they want them. No other part of their rifle is touched by them. The rifle recoils exactly the same from shot to shot and the bullets leave the same way each time.