"I have replied today saying that while police [are] not permitted to pass on details covered by the Clean Slate Act to a third party, I am waiving my right, to disclose a conviction for drink-driving.
"The incident happened 34 years ago while I was an off-duty detective constable in Auckland in 1983.
"I pleaded guilty and was convicted. I received a $250 fine and was disqualified from driving for six months."
Bush was 23 at the time and had been a police officer for five years.
"I didn't lose my job at the time because it wasn't until 1991- eight years after it happened - that the then Commissioner of Police made it clear that subsequent drink-drive convictions for a police officer could place their career in jeopardy," Bush said.
"It was extremely poor judgment by me 34 years ago, for which I am sorry. I make no excuses. It is something I deeply regret and have reflected on ever since."
Bush said his name and occupation were reported in an Auckland newspaper at the time, as was standard for drink-driving cases back then.
"Many of my colleagues and friends are aware of it, and it was disclosed to the State Services Commission as part of the process for appointing me Deputy Commissioner and Commissioner," he said.
"I have always been prepared to talk about it if asked."
Bush said since his conviction there "has been a significant change to New Zealand's attitude and culture regarding drink-driving".
"Police has had a big part to play in driving that change.
"Alcohol plays a significant role in death and injury on our roads, and I am personally committed to doing all I can to prevent the harm it causes."