Rimfire rifles are very susceptible to impact changes caused by different degrees of pressure on the stock. Your rifle should shoot Ok resting over bags, after all that's what the bench rest fraternity use.
However you must take care to be consistent with other points of contact, possible causes of your poor grouping can be variances in rifle butt to shoulder pressure, cheek to stock pressure and then hand to pistol grip which tends to have more variance and influence the higher the trigger weight is. In your first group, the fact that you noticed the differing recoil which resulted in the high right shot indicates there are some pressure variables on the stock. It is also important that when squeezing the rear bag that you are not subconsciously moving the rifle onto the aiming point, let the bag take to weight of the butt.
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