NEW YORK — School busing contracts that were opened up for public bid last spring and awarded in May will save the city an estimated $210 million over the next five years, the New York City mayor and education chancellor said on Monday.

The savings is in addition to the $100 million saved from bids awarded last winter and the $95 million saved from pre-kindergarten contracts that were publicly bid in 2011.

But the contract bids were not without opposition. Early this year, New York City’s biggest school bus driver union went on strike for more than a month, calling for the continuation of job protections, but Mayor Michael Bloomberg maintained that the city was "not legally allowed to provide” those job protections.

The busing contracts had not been open to public bid since 1979. From that year to 2011, when the city put out its bid for pre-kindergarten contracts, the cost for busing skyrocketed from $71 million to $1.1 billion per year.

“When we released the bids for new bus contracts, we broke a three-decade stranglehold that exploited taxpayers and took money out of the classroom, where it belongs,” Bloomberg said on Monday. “The bids we received surpassed our savings estimates and give us more money to invest in ensuring New York City schoolchildren are receiving the best education possible.”

The mayor also announced plans to place the expiring contracts for an additional 4,100 bus routes up for public bidding. These routes serve about 39,000 students with disabilities and 96,000 general-education students. City officials expect the public bidding to save hundreds of millions of dollars.

“We are continuing our effort to find savings by bidding out new bus contracts, and our preliminary review of the new bus bids released in April show an estimated savings of $210 million over five years,” said Dennis Walcott, chancellor of the New York City Department of Education. “This is our third request for bids since 2011, when we said that through a robust competitive bidding process we would anticipate savings while maintaining the highest standards for safe and dependable yellow bus service for our students.”

In total, the Department of Education has contracts that cover the school year for 7,700 bus routes that serve 152,000 students, 54,000 of whom have disabilities and require special transportation services, plus about 1,650 routes that run during the summer only.