Bench rest and double rifle don't seem to go together. For sure, ALWAYS make sure the rifle is resting on your hand, even under a bag. I know you're looking for accuracy from a bench for load development, but it's not the way you'll hunt. Once you've found a 'possible' load go sitting like off x-sticks (again hand under forend) and seen what you can duplicate. Or try standing with hand between 2x4 and rifle - I prefer sitting.
Another note, I've found and learned that the Best makers took the time to regulate doubles to give good groups, lets say 2" at 50 yds. While a lot of other makers seemed to be content with a group that's double in size - no matter what you try as a load. No different than today, time vs $ in a building a firearm.