My process is to cut the blank down to size first, before drilling. Makes it easier to make sure you have enough bit length, and avoids how far off the bit might drift by the time you get to the other end, if the bit drifts.
My overall process for pens is as follows:
1. Cut blank(s) to match tube lengths.
2. Drill cut blanks. I'll use a drill press for speed if getting exactly centered drilling isn't necessary, or the lathe if keeping the hole as centered as possible IS important (sometimes this is important with segmented/layered blanks).
3. Paint tubes and holes as appropriate, if necessary.
4. Glue tubes into blanks (usually with 2-part epoxy, but sometimes with gorilla glue if I find I need to fill space around a loose tube.)
5. Trim blanks to tube ends (usually with a disc sander and pen squaring jig.)
6. Turn blanks to size and shape down to bushings (usually between centers, unless the bushings require a mandrel.)
7. Sand turned blanks to high grit (pretty much always, wood or reins, I sand to a high grit/high polish. To 2000 grit or wood, 12000 micromesh or 1 micron zona paper for resins.)
8. Finish blank (walnut oil/pens plus usually for wood, ultra high grit plastic polishes for resins; possibly buffing if necessary to get optimal shine.)
9. Assemble pen.