Local 1181 President Michael Cordiello said the city is unnecessarily prolonging the strike.
Two men were arrested Wednesday as the Amalgamated Transit Union kicked off their strike, police said.
Tens of thousands of parents tried to find other routes to school Wednesday morning.
School bus drivers are planning to begin picketing Wednesday morning.
The bus drivers' union is planning to strike on Wednesday.
School bus drivers were on the roads Monday morning, but could still strike later this week.
Union leaders accused the Bloomberg administration of putting cost-saving ahead of bus driver quality.
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