City school bus companies and union leaders have been meeting in an effort to resolve the strike.
A mediator was conducting the meeting at the mayor's official residence, Gracie Mansion.
The strike by school bus drivers and aides entered its eighth day Monday.
The conflict is over the city's need to rein in spiraling costs against the bus drivers' goal of keeping their jobs.
The city contracts with private bus companies. It says the city must seek competitive bids to save money. Local 1181 of the Amalgamated Transit Union wants the new contracts to include job protections for current drivers.
Some buses have been running because their drivers are not members of the union.
The city's last school bus strike, in 1979, lasted 14 weeks. Bloomberg said at a news conference last week, "I hope this is not going to last a long time but it's not going to last past June."
