Remove the bolt and bore-sight while looking down the barrel. Align the cross hairs on some tiny spot way past 100 yds (the farther away the better), while at the same time, centering that same tiny spot in the barrel - while looking down it. I like to use a neighbor's pole light at night that's about a mile away.
When I can do this I'm always on the paper at 100 yds.
Another thing to do is mechanically center your scope. Count how many clicks are in the full range - max low to max high, and max right to max left - then divide that number in half and put the cross hair at that many clicks. That lets you know how out-of-wack your rings/base are.
Ideally, every thing should align pretty close with the scope mechanically zeroed like that. If not, then that's when it's time to start playing with the rings and base - shimming, sanding, replacing. You want that rough mechanical zero as a starting point.
Sometimes just swapping the rings, front to back, back to front, will have some benefit. Or flipping a base around (if possible, depending on the design, of course).