OP,
Folks just getting into shooting today usually start out with a scoped bolt action rifle " rested" with a bipod. They perceive their equipment will get them to the promised land. However, not having any formal marksmanship training, or exposure to what's really important to good shooting, problems, such as what you have described, are certain. These problems begin as soon as the rifle is shouldered by an anxious shooter who wants to get the reticle on the target, rather than first just allowing the rifle to point where ever natural. This brings about a chain of events which collectively assures the rifle will be pointed somewhere other than where desired as the bullet clears the bore.
As has been alluded to in earlier posts, the shooter needs to first learn how to build a position which transfers the stability of the ground into the position through bone and artificial support, muscular relaxation, and adjustment of natural point of aim. From there, making grip, butt-to-shoulder, non-firing hand, stockweld, and elbow placement consistent will assure control, the bottom-line of a steady position.
Practice building a position built on bone alone helps the shooter to understand when bone indeed is supporting the position. Beginnning with a bipod dulls the recognition of muscular relaxation and thus a natural point of aim may not be realized, leading to the sort of problem you are experiencing.
As 308boltgun suggested, take a look at the marksmanship tips from the USAMU. You may also want to attend the USAMU SAFS (Small Arms Firing School) this July 26, 27, & 28 at Camp Perry for hands on instruction.