It may be that skim bedding the block would help. Also, is the barrel touching in its channel anywhere?
On the scope base or bases, the screw nearest the front of the action can sometimes be bottomed on the barrel shank, if it is too long. If this is the case, the base will not be properly clamped to the receiver, even though the screw is tight. I always count the turns (and partial turns. of any screws that go into holes that are not open on their bottom ends, with and without the thing that is being attached in place (in this case, the scope base(s)) There should be fewer turns (at least a half) with the base in place, as compared to when it is not.
Another thing to try is to pile up sand bags, or borrow a front rest, instead of the bipod, just for a test. If you try this, I would support the rifle a couple of inches in front of the action. Bipods that are mounted where the typical front sling studs are can cause the rifle to "hop" when shooting off of a hard surface. I have found that in some cases putting something with a little give (like one thickness of a cheap soft rifle case) under the bipod legs can be beneficial.
Another thing to look for is whether the rear sling stud is clear of the back bag. (It should be.) Also, the back of the pistol grip should not contact the rear bag at any time.
How are you holding the rifle? If you hold it too light, there can be problems. Sometimes shooters try to imitate a shooting style that is OK for a lighter caliber, or a heavier caliber in a heavy benchrest style stock, with a rifle that is too light and/ or a stock that is the wrong shape for that shooting style. I would shoulder your rifle, have my face lightly on the comb, and pull it back into my shoulder with the second and third fingers of my trigger hand. I might even try light contact with my other hand just forward of the action. Sometimes experimenting with how a rifle is shot can yield better groups.
Another thing to watch is barrel heat. The barrel should never get too hot to comfortably hold your hand on the hottest part.
If you want to use your magazine, you may not be able to seat your bullets out any farther, but if you can, I usually get my best groups with them seated .006 to .010 longer than where they touch the rifling. (light marks). You should lower your powder charge and rework your load if you try this, because of the slight increase in pressure.
What scope are you using? Does it have a parallax adjustment?
