The incident happened in September as Ms Bishop was travelling to the United Nations General Assembly in New York.
The officer who conducted the pat-down was suspended and later reinstated.
But a more senior officer who ordered the check has been sacked. The airport said the check had not been random.
The female airport worker who carried out the screening was found to have not adhered to "standard security screening procedures" but was reinstated after receiving training.
The Sydney Morning Herald reported that at least three other airport workers have also been suspended.
The foreign ministry made clear it did not make an official complaint.
It later emerged that Deputy Prime Minister Warren Truss had asked ask the airport to investigate, says the BBC's Jon Donnison in Australia.

Hutchinson is involved in metal design and manufacturing and laser cutting.
The jobs will be recruited over the next three years. A further 40 new jobs have been filled in the past nine months at the company.
The jobs consist of manufacturing roles, business development and sales and marketing.
It is part of a Â£4.1m investment supported by Invest Northern Ireland.
The investment includes the expansion of the company's Kilrea site and further investment in laser technology with the addition of two new lasers.

The Queen's cousin, 79, was taken to Aberdeen Royal Infirmary on Monday after he suffered the injury while staying at Balmoral.
He was seen walking to a waiting car with the help of a walking stick.
The duke, who undertakes a large number of official royal engagements and has close associations with many charities, suffered a "mild stroke" in 2013.
He is perhaps best known as president of the All England Lawn Tennis Club, in which capacity he has presented trophies to winners at Wimbledon.
He is also grand master of the main organisation of Freemasons in England, the United Grand Lodge.
He became Duke of Kent in 1942 at the age of six after his father, brother of King George VI, died in an RAF plane crash.
Balmoral is the Scottish home of the Royal Family.

Simmons, 52, was suspended in September for questioning the continued omissions of Dwayne Bravo and Kieron Pollard.
He issued a public apology to the West Indies Cricket Board (WICB).
"I regret my public outburst during a press conference and the revelation of the vote that took place at the selection meeting," said Simmons.
"I extend a public apology to all whom I may have offended. I have personally apologised to my fellow selectors and the WICB and now do so again publicly.
"I am looking forward to putting this behind me and doing the job I enjoy with the West Indies' senior men's teams."
Simmons played 26 Tests as an all-rounder for the West Indies between 1988 and 1997, and became head coach of their senior squads in March.
Eldine Baptiste took over from Simmons for the current tour of Sri Lanka, with the West Indies losing both Tests and all three one-day internationals before Wednesday's concluding Twenty20 match.
An Australian security officer at Melbourne airport has been sacked after the country's Foreign Minister Julie Bishop was reportedly singled out for a security screening.
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Forty jobs are being created in Kilrea, County Londonderry, and in Antrim town, by manufacturing company the Hutchinson Group.
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The Duke of Kent has left hospital following successful treatment for a dislocated hip.
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West Indies have reinstated Phil Simmons as head coach of their senior squads after he apologised for criticising team selection.