Sometimes/mostly every time when shooting from the bench, at 100 yards, at target dots on a ~24" X 24" paper, the zero moves as I go from target to target. First target might show a zero 2" directly below the dot- Second dot maybe 4" to the right of the first, zero is now 3" below and 1" right of the dot. Etc. The group centers move as the gun is aimed at different dots. 
Does anyone know why this is, and/or how to eliminate the effect??
Thanks;
joe b.

The amount you are stating seems awful extreme. When changing from bull to bull you need to make minimal disturbance to your set up. Any change in the way the gun is resting and responds to the recoil will affect your point of impact. Do you free recoil or hold your rifle when shooting bench. Depending on stock forearm design you may not be able to free recoil. The key is to minimize variation (which includes frictional variations as well as pressures applied).  Try baby powder on your front bag if you don't already that will reduce friction variations. Thats my two cents good luck

Joe,

I agree with what has been said, but I want to add that when going from one target to another, if you take your time laying out bullets and primers, etc., it's a good idea to put a shot in the bank so your lube is soft and the barrel is not cold, if that happens I usually get a high shot. 

Bob

When shooting from the bench, the group center moves as I go from dot to dot. The targets I’m talking about are 24” X 24” pieces of paper with sets of dots spaced ~ 4” apart, so a set might be, from the left edge of the paper, at 4”, 8”, 12” 16” and 20”. Sets might be spaced 4” apart in height. 
My impression is that generally the group center moves in the direction the gun is moved. If the rifle is moved left to shoot at a dot to the left of the last one, the group center will move to the left. This is merely an impression, not any kind of rule. Sometimes the group center moves up or down when the gun is aimed at another target.
I’d like to know why this happens, and how to cure it.
I have no guns with “bench rest” 3” wide forends. 
I use a Hoppes front rest with a Stoney Point Universal Front Bag, (4.75” L X 2.5” H X 2” W), and a Protektor rear bag. The front bag is attached to the Hoppes rest with double-sided tape and the Velcro holder things. The front rest is free to turn left and right, the top piece is free to rotate on the shaft. Everything else is locked down. Coarse elevation adjustments are made on the Hoppes front rest; fine elevation adjustments are made by sliding the gun forward and backward.
Clearly, windage adjustments are made by moving the rear bag left and right.
I put baby powder on both front and rear rests frequently, to keep
I have considered getting one of the very expensive bench rests with the precision windage and elevation adjustments, but so far have been able to control myself.
First, the windage adjustable front rest, it seems to me, puts “different” forces on the forend as it is adjusted right and left. Torques the forend.   
Second, I can shoot small groups with the rests described above, consistently shooting under 1” five-shot 100 yard groups with rifles capable of that, so neither my rests nor my procedure is grossly wanting. I think. 
I took my question to some forums, and got a variety of responses. This response let me know that my experience is not unique/I may not be nuts:
“It's a common problem when shooting at multiple bull targets. That is one thing that makes shooting a 250 on the 100 yard ASSRA bench target more of a challenge then one would think it should be. I always suspected it had something to do with the position of the rifle on the sandbags but it could also have something to do with how the rifle is held from the slightly different positions. It also could be that wind conditions change as the target is being shot. I have been shooting single shots a long time and I don't know for sure. Maybe some of the others who are more expert then I at rest shooting can give you the answer. I would like to hear from those that shoot "free recoil" to see if that helps.”

The more credible of the suggestions:
“…after each shot, move the rifle back and forward in your bags. This will settle the rifle in the bags the same each time. I move the rifle forward and aft about three time each time, just before I get ready fire.”

“…slide the rifle firmly in the bags to reposition when moving to a new target. After pushing down on the rifle when sliding it in the bags after aiming at the new target; confirm the rifle is sitting squarely on the bullseye without any body pressure on the rifle.
…Rule number one is to ensure the rifle is sitting in the sandbags pointing perfectly at the new target's bullseye before I assume the firing position. And that the position is stabilized by walking the rifle in the bags to ensure it is sitting perfectly before you assume your bench shooting position. 
…the next best rule is to ensure you pull straight back on the trigger to prevent any side torque from slight pressure from pulling on the side of the trigger… 
…If you don't walk the rifle into the bags it will be following the same path established from the recoil from shooting the previous targets; and you can get the rifle recoiling slightly off center until it re-establishes a realignment of the sandbags on subsequent recoils. “

These mean to me that after shooting one group, re-set the rests and “mash” the gun into the bags to get it settled in and aimed at the next dot. This rather than looking through the scope and moving the rear bag to get aimed at the next dot. A new beginning, a new set up, for each dot shot at. 

Anything I missed? Anyone?
Thanks;
joe b.