Schools Chancellor Dennis Walcott said the strike started at 6 a.m. Wednesday. About 200 bus drivers and bus matrons, who help kids on and off buses, were assembled on picket lines in the Queens section of the city.
"The first days will be extremely chaotic," Walcott told 1010 WINS radio. "It hasn't happened in New York City in over 33 years."
The union did not immediately return calls and emails seeking comment.
Matthew Mosca said his 5-year-old daughter, Ella, usually takes the bus from their home on Manhattan's East Side.
On Wednesday, they took a taxi.
"It's an inconvenience but I support the strike," Mosca said.
On Staten Island, parent Alicia Vuscemi had more scrambling to do, with kids at three different schools. Her son attends school in Brooklyn, and she got a pleasant surprise when his bus arrived. "I was still trying to figure out how he was going to get there," she said.
But she was concerned at the prospect of a lengthy strike. "Is it really going to last a while?" Vuscemi said.
Wednesday's walkout was by the largest bus drivers' union; some bus routes served by other unions were operating.
Most of the city's roughly 1.1 million public school students take public transportation or walk to school.
Those who rely on the buses include 54,000 special education students and others who live far from schools or transportation.
Parents have made plans to use subways, carpools and other alternatives, hitting slippery roads as sleet turned to rain around the city and temperatures were at or above freezing.
The city has put its contracts with private bus companies up for bid, aiming to cut costs. The Local 1181 of the Amalgamated Transit Union says drivers could suddenly lose their jobs when contracts expire in June.
The city plans to distribute transit cards to students who could take buses and subways and to reimburse parents who would have to drive or take taxis.
"We will get our children to school," Walcott said.
To do that, some parents had pieced together a patchwork of plans, such as a driving one child to one school and arranging a carpool to take a sibling to another school.
The union announced Monday it would strike amid a complicated dispute.
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 union President Michael Cordiello.
Mayor Michael 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.
Asked if the city is prepared to go as long as the last school bus strike in 1979 which lasted 14 weeks, Walcott said on WINS Radio, "This will go however long it goes. We have systems in place to support our parents and students."
Walcott, who was making the rounds of radio and television news shows Wednesday morning, told WNBC-TV there were no talks scheduled.
"We're not negotiating. They want us to do something illegal. We can't do that at all. We're always open for communication ... It's not our responsibility and job to negotiate. They work for private companies."
Asked if the city planned to take the striking union to court, Bloomberg told Fox 5 New: "I don't think it's time to do that" and characterized the union's actions as illegal."How is it illegal to provide the most experienced drivers and matrons in the school buses?" Cordiello asked Tuesday.
The contracts expire June 30.