Seeking a speedy end to the strike, a consortium of 20 bus companies filed two complaints with the National Labor Relations Board on Wednesday accusing the union of waging an unlawful secondary strike and of not bargaining in good faith.
"We are asking the NLRB for an immediate ruling," said Carolyn Daly, a spokeswoman for the bus companies.
James Paulsen, director of the NLRB's Brooklyn office, said the board is reviewing the complaints.
He said that if the NLRB finds that the union is pursuing an unlawful secondary strike, it will seek a federal injunction to halt the labor action.
The city doesn't directly hire the bus drivers and matrons, who work for private companies that have city contracts. The workers make an average of about $35,000 a year, with a driver starting at $14 an hour and potentially making as much as $29 an hour over time, according to Cordiello.
Bloomberg has said the city must seek competitive bids to save money.
The union sought job protections for current drivers in the new contracts. The city said that the state's highest court, the Court of Appeals, has barred it from including such provisions because of competitive bidding laws; the union said that's not so.
The dispute pits two seemingly irreconcilable imperatives against each other: city budget constraints and union members' desire to keep their jobs. Absent an injunction, the strike could last a long time, observers on both sides of the issue said.
"I don't see the city backing down," said John Hancock, a lawyer with the firm Butzel Long who has represented Michigan school districts in teacher strikes. "It's not so much a labor dispute. It's blackmail."
But Ed Ott, the former head of the New York City Labor Council who is now a distinguished lecturer in labor studies at the Murphy Institute at the City University of New York, said, "From the workers' point of view, the bidding process leaves them no option but to fight for their jobs ... They kind of have their backs to the wall."
The city's last school bus strike, in 1979, lasted 14 weeks. Bloomberg said at his news conference, "I hope this is not going to last a long time but it's not going to last past June."
Associated Press writers Eileen AJ Connelly and Verena Dobnik contributed to this report.