I'm not familiar with this particular screw so this may be out of "left field". In general, such screws usually go through the stock and screw into the trigger plate and were often tapered, as well. In addition to the bushing suggested by SKB, it is often helpful to align a "center"(fitting the hole in the trigger plate) with the twist drill in the chuck. Having the intended hole so "located" at both ends usually helps the process. The tapered screws were usually "burned in" for the purpose of making a precise fit between the screw and hole, to keep the stock tight against the action. I wouldn't be surprised if instead of "burning in" these screws, some replacement stocks are installed by "glassing in" release agent coated screws instead. As usual some may find fault with this, and it wouldn't hurt my feelings.
Mike