I've never had a problem counterboring, even with my little chinese tabletop drill press. Just use a 3/8" top quality 45 deg. (standard) bit at the proper speed, set the barreled action up clamped vertical and parallel to the drill and so the bit will swing out right over the bore center. Make sure the drill is fairly tight, minimal wobble. Use plenty of cutting fluid or motor oil to keep it cool, make short cuts under enough pressure to cut the bore continuously. if you're too cautious and let it rub instead of cutting it'll just get hot. Pull the bit out and inspect for good rifling around the cut. When you hit decent rifling you're done. Knock any chips off with a piece of brass or plastic.
I've never had a problem centering either because the 45 deg. drill bit really wants to go right down the center of the bore or maybe because I'm so anal retentive I get it perfectly centered and straight. I've always gotten back within 3 moa. ( about 3 in group at 100 yds, benchrest, sandbags.)