Here is a method that has worked very well for me. First, clean everything thoroughly. That includes the screw holes, screws, etc. Get everything clean. Don't forget the scope tube. Everything means everything. Next put a drop of Locktite on the threads of the screws and install the bases. Us a correctly fitted screw driver. Snug the screw up, but don't use good common sense and don't use so much force that you wring the screw off. Next, the bottom of the rings on the bases. Again, use common sense. Install the scope and the tops of the rings. Orient the scope to vertical before you tighten the screws down firmly. Depending on the ring set used, you may need to tweak things a bit to get the scope correctly in position relative to the bore of the rifle. Also before you tighten everything down for eternity, make very sure that you have the scope positioned for comfortable safe use when employing normal shooting positions. Given that no one normally has a bench-rest in the woods/fields, check to see that you can comfortably and safely use the rifle/scope when firing from the prone, sitting, kneeling and standing positions. You will have to compromise how your locate the scope as the ideal position for prone will not be the same as what would be ideal for sitting, kneeling or standing. It will be close. You'll figure it out.
Using the above method I've mounted scopes on rifles that have held their zero for many years. The only times I've ever had a problem is when I failed to follow this procedure. Hope this helps. Sincerely. bruce.