I shoot benchrest...
Vertical stringing is load - You're not tuned to your rifle's sweet spot.
Horizontal stringing is operator error. Could be several things. Wind is one. You'll be surprised at how much a group can vary at 100 yards, even on a "calm" day - a few mph wind going one way can switch to a similar speed in the other direction, and before you know it, you've shot a 1" group... (and we use 68 grain bullets, moving at about 3400 fps...). Get some coathangers and strips of surveyor tape, and stake a few out, maybe at 25, 50 and 75 yards (if shooting 100 yards), and only shoot when they all point in the same direction, at the same intensity. You'll be surprised.
Could also be how the rifle is supported - can it slide freely on the bags? Does it track straight back, or is it moving side/side when you pull it back? Is your shoulder placement consistent? Are you holding it the same way ever time? Are you pulling the trigger the same way every time? A lot of times a stiff trigger will result in horizontal, since you're putting pressure on the stock there...