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I don’t have room to lay a bike on its side on a pillar drill, tbh. That would be ideal but doing it by hand is fine. I just use WD40 or Rothenburget cutting fluid and apply it gently over the drill tip from above. As @maynardeames says, you don’t need much, on a small job like a bolt it just helps preserve your drill bit and stops it from snatching. It does help if someone else applies it while you have both hands on the drill, tho.
Daft question: how do you supply cutting fluid to something like this - I presume in a bike shop you'd use a pillar drill on a workbench? I know machine tools usually have a cutting fluid feed that you can point at the workpiece, but what would you use in this situation?