I drill all my blanks, after rounding between centres, on my metal lathe using a Collet chuck.
I follow the centre drill with a "Pilot" drill which just clears the web at the centre of the point of a twist drill. I usually use a #40 drill for this.
The Pilot hole keeps the final drill central ( concentric) for the first 1.5 or so inches and results in a through hole which exits on the centre of the bank beautifully.
When drilling the pilot hole watch the shank where it enters the blank and withdraw it immediately it starts to spiral as this indicates the tip is wandering due to swarf build up at the tip.
For acrylics I limit myself to 1000RPM for the pilot and 400 RPM for the final drill. I withdraw the drills every three turns of the tailstock wheel (approximately 0.2inches). I unlock the tailstock and pull the drill straight out of the blank, clear the swarf, and push it back in without stopping the lathe (the quickest way I've found) I cool the drill with Alcohol (Methylated Spirits in the UK) after each withdrawer keeping the drill cool to prevent seizing/blowouts.
Follow the pilot drill with the full diameter drill required DONT enlarge the hole in steps as this causes non-concentricity.
Hope all this helps somebody.
John