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2. It's not uncommon for me to have the POI for a group to shift simply as a result of a change of hold technique--for example changing from bags on a bench to prone with a bipod. I tend to "hover from above" when leveling and making the changes--only periodically looking through the scope to check the true during the setting process--it occurs to me that in the truing process you might need to "simulate" your intended actual shooting position as closely as possible, cheek weld, trigger hold etc (?).
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Let me help you with this.. Its not you and it's not uncommon. When we build precision rifles we do everything we can to remove all the factors that can change the normal harmonics of a rifle barrel when it's shot. If your rifle is off the shelf and you haven't done anything to improve it, then changing from bags to a tripod can change the harmonics and will affect your groups. Bags should give you the best grouping because it is the closest to off hand shooting which is what the rifle was designed to do.
My suggestion is to first check the bottom screws in your rifle. To do this, loosen them fist. Next, tap the rifle butt on the floor a couple of times and then while still holding it vertically, tighten the rear screw to 35 inch lbs and then the front to 35 inch lbs. If your stock has aluminum pillar posts you should torque to 65 inch lbs. Make sure you have pillar posts if you go to 65 because you can damage your stock if you don't.
Next, remove your bipod and shoot off of bags. That will let you know how the rifle really shoots and you can start trying different ammo to make it better.