BigSteve22 said:
The only way I've ever seen to correctly counter bore an existing hole, using a drill press, is with an index.
That'll work. I've had to drill string-through holes a number of times, so I do it a slightly different way with a simple indexing jig. Get a board larger than the body, clamp it to the stage and drill a single blind hole in it the same diameter as the string holes at the face side of the body. Then you break off a cheap or dull bit of the same diameter to make an indexing peg. Put the peg in the hole so it sticks up 1/4" or so. Then you can place the body face down so the peg fits into a string hole and your quill will automatically be aligned with the center of the hole. Drill the counterbore, then lift the body off the pin, move it to the next hole and go again. Keep doing that until you run out of holes.
I originally did it that way for drilling holes all the way through the body, as it's risky to drill all the way through from one side if it's important that the holes be perpendicular. Chances of the bit wandering off-center on its way through are high with smaller diameter bits. So, you drill partway through on one side, then use the indexing jig to drill from the other side to meet the hole. The same jig is then used to do the counterbore for the ferrules.