im betting your rifle has stress in the action or on the barrel. Changing from a solid bench rest to a bi-pod should'nt throw a group, It may change Point of impact because of the difference in shooting form, but shouldt open up a group (at least not alot).
I would ensure that the barrel has a proper free-float. If it has an injection olded stock, fold a piece of thick computer paper twice (4x the thickness of the paper) and make sure that it slides all the way down from the tip of the fore arm to just infront of the recoil lug. If it has a good wood or fiberglass stock the clearance can be half that.
To ensure that your action is stress free have it bedded (if not done already) and make sure that your action screws are set to the correct torque.
If you have an injection molded stock you may need to stiffen the foreend with old arrow shafts and epoxy. when the full weight of the rifle is on the very tip of the forend (as with a bi-pod) there can be a substantial diffrence in stress on the stock form when its on bags. with fiberglass the forend is much stiffer and you can count on the stock not hitting the barrel. This is especially important when you have a rifle with a heavy barrel and big optics.
One of my rifles has an injection molded stock, and I have 3/16 per side. I can see that sometimes the gap is bigger on one side compared to the other, then moves back to normal with temp. changes.