Sometimes the base screws are too long and even though they appear tight, the base is not. First, i verify each base screw will firmly hold the base to the action separately. If i find a long one i carefully sand it down with very fine Emory cloth until it fits. I use blue loctite on base screws.
Burris has a good ring called a Signature Zee. They have an insert that really helps prevent scope movement in the ring
http://ads.midwayusa.com/product/612...ngs-matte-high
The revolutionary Signature design produces consistent accuracy, tremendous gripping power and stress-free mounting. These steel rings include a pivoting synthetic insert that increases the scope-to-ring mounting surface while protecting the scope finish. Additional Pos-Align Offset Inserts can be purchased (sold separately) to correct any misalignment of receiver holes or rings or even to provide additional windage and elevation adjustment.