Another cause of crosshair movement is not having the proper eye relief for the scope.
What Brian said is good advice. Mount the scope fairly loose so you can slide the tube forward or aft.
Mount the rifle and if the scope has a lot of dark around it, move your head back and forth until the view "blooms" and is clear all the way to the edge.
Move the scope forward or rearward to get that sight picture without having to hunt for it.
Then you can snug the scope up making sure the reticle is square.
Once you have the scope mounted solidly, then you can bore sight.