The five Sikh tourists from Birmingham were ordered off the bus on Sunday with their hands bound behind their backs after a tour company employee called police to report that they seemed suspicious.
The police cordoned off the block for 90 minutes, ordered all 60 passengers off the bus, and searched their belongings and then their bodies. The five men were then identified by the employee and cuffed.
New York has been on heightened alert since the London bombings and police recently started checking bags in the subway.
Mr Bloomberg advised New Yorkers to use common sense when reporting anything suspect and to avoid profiling people.
"It turned out that these people did not present any threat whatsoever," he said.
"The police, who have to react in this day and age and take evidence at face value, had a show of force that probably doesn't make good reading in the paper.
"It's a shame, and I certainly apologise on behalf of the city of New York."
The tour bus company, Gray Line, stood by its supervisor. "We have trained our employees to report suspicious activity to the police," its spokesman, David Chien, said. "That is all we did."
After the terrorist attacks of September 11 more than 400 Sikhs were attacked across the country, claims Amardeep Singh, legal director of the Sikh coalition in New York.
He said reports "across the board" showed Sikhs were being confused with Arabs and other Muslims.
One of the tourists, who have since left New York, said the incident had not spoilt his time in the US.
"These things happen, don't they," the 39-year-old man, who gave his name as Jas, told the Daily News. "We have no hard feelings."