A surprise strike today by disgruntled Boston Public Schools bus drivers sent thousands of parents scrambling to find alternative ways to get their children to and from school. The mayor announced that students could ride free on the city’s transit system, if they needed to, while police took the unusual move of scouring the streets, picking up stranded students and ferrying them to school.

City officials said tonight they hoped that the strike wouldn’t stretch into a second day and that drivers would show up for work Wednesday morning, but they weren’t sure — and they suggested parents again make alternative plans.

“If they really care about the students of Boston, they’ll show up for work tomorrow,” said Mayor Thomas M. Menino, who said he was “extremely angry” at the “illegal work stoppage” by the drivers. “Our young people should not be hurt because of selfish people who only want to cause disruption in this city.”

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He said free MBTA rides would continue to be offered Wednesday for students and schools would open an hour early to accommodate parents dropping off their children.

The drivers in United Steelworkers Local 8751 are locked in a dispute with Veolia, the transportation contractor providing the bus service for the city. The company sought a federal court order late this afternoon that would have required the drivers to return to work.

US District Court Judge George O’Toole declined to issue the order, saying the contract allowed for the union to have time to tell its employees to return to work. But he told the parties gathered in court, “We may see you again tomorrow.”

Steve Kirschbaum, chairman of the grievance committee for the local, which represents approximately 700 school bus drivers who work for Veolia, said the job action reflected the drivers’ frustration at the way they’ve been treated since Veolia took over the busing contract this year.

He said the drivers’ grievances include changes in their health care plan, payroll problems, and new procedures instituted by Veolia.

With only 30 of the system’s 670 buses taking to the road, according to school officials, absenteeism nearly tripled, rising to 9,600. About 33,000 of the city’s 57,000 students take the bus to school.

Interim School Superintendent John McDonough said, “Today has been incredibly difficult because of this work action. We do not know for sure if it will extend until tomorrow so we are asking parents to make alternative plans.”

He said students who couldn’t make it to school today and those who can’t make it to school Wednesday because of bus problems would be marked “Excused.”

Menino said at an earlier news conference that Veolia was simply implementing what was in a contract that the drivers had agreed to. He described the union as “rebellious.”

“They want to do whatever they want,” he said.

“The items the union is resisting are sensible, core practices … to ensure safe, on-time, and quality service for passengers,” said Jonathan Sander, an assistant general manager for Veolia, who appeared with Menino and other city officials at the news conference.

Union officials at a protest at a bus yard in Readville provided a Globe reporter with a National Labor Relations Board complaint they had filed.

The complaint listed a host of issues, saying, among other things, that Veolia had refused to bargain with the union, had unilaterally implemented changes to terms and conditions of their contract, had refused to recognize their union and its officers, and had refused to abide by the grievance and arbitration process.

But a divide appeared as the day wore on between union leaders and the rank and file.

The United Steelworkers released a statement calling on its local to return to work.

“The USW does not condone the current action, or any violation of our collective bargaining agreement, and has instructed all members of Local 8751 to immediately cease this strike ... and resume work as soon as possible,” USW District 4 Director John Shinn said.

When local president Dumond Louis, addressing the workers at the Readville bus yard this morning through a bullhorn, asked the workers to go back to work in the afternoon, he was greeted with boos and shouts of “No!”

“We have to do it legally,” he tried to tell the dozens of workers, but he was drowned out by opposition from his own membership.

Drivers at the Readville yard this afternoon again shouted down Louis when he said he had been unsuccessfully trying to meet with management and he wouldn’t resign.

The drivers also shouted down a representative of the United Steelworkers when he told them they were acting illegally and they needed to work Wednesday.

Albert Polk, the Steelworkers official, said in an interview that he couldn’t force drivers to go back. “All I can do is ask,” he said. “This is a free country. I don’t see anybody in chains.”

The divide came into sharp focus at the federal court hearing when union lawyer Patrick Bryant, arguing that the union should not be the subject of a court order, said the union had actually opposed the strike, which he called the work of “rogue” employees staging a wildcat strike.

At the Readville bus lot this evening, workers cheered when they learned that the judge had declined to issue the order.

“If we get Veolia Corporation to come and meet with us and resolve our legitimate issues. .. we’ll be driving the buses tomorrow,” said the outspoken Kirschbaum. “If we don’t hear from them, we’ll make our determination in the AM. There’s a lot of hours between now and then.”

At another bus yard on Freeport Street, Frank Connolly, 46, of Quincy, who has been driving buses for 26 years, said his fellow workers were prepared to go back to work this afternoon. After missing the morning run, they knew it was time to return to the job in time for the end-of-school release.

But, he said, when they returned to the yard, they found the lot shuttered by the company. “They heard what we said and they began to lock the gates and push us off the properties,” Connolly said.

“We’re being told that we’re violating the contract — as soon as they stepped in here in June, right off the bat they were violating our contract. They never even agreed to the contract,” Connolly said.

Schools spokesman Brian Ballou said officials had heard rumblings about the strike and had placed monitors at bus yards this morning, who learned shortly after 5 a.m. that the strike was underway.

E-mail alerts and automated calls were sent out to all families with children in the schools in hopes that they could arrange alternative ways to get to school.

Schools spokesman Lee McGuire said the work stoppages happened at all four of the system’s bus yards.

He said the bus drivers’ complaints included increased GPS monitoring of where school buses are.

“This is 30,000 families who had to scramble at the last minute this morning to find alternative transportation,” he said.

Lisa Jones, a driver since 1988 and the union steward at the Readville yard, said she didn’t know when the stoppage would end.

“I don’t know if the membership is going to do it or not,” she said. She insisted that the work stoppage was not a strike, it was a “protest” instead.

Jones said she had filed more than 200 requests for the company to fix payroll and paychecks because of errors by Veolia. She said some drivers did not get paychecks at all Friday and are still waiting to be paid because of the company’s flawed practices.

Jones said another problem at the Readville yard was the decision by Veolia to fire a long-time manager who has been effective in working with bus drivers.

At the Blackstone School in the South End, one elementary student stepped out of a police car this morning. Principal Danielle Morrissey said others also had been delivered by police. The school has 640 students, 70 percent of whom are bused, including 250 who come from East Boston and 35 with multiple disabilities who require specialized buses. No buses had arrived this morning. She said she expected a lot of absences, but the school would continue operating.

“It’s business as usual. We’ll teach the kids in front of us,” she said. “It’s tough for families to get here without the school bus transportation.”

Nelson Foster walked from Dudley Square to the Blackstone, with several other family members, to drop off his 7-year-old son.

“I don’t think the word ‘cumbersome’ sums it up,” he said. “It’s an inconvenience for everyone.”

At the Ohrenberger School in West Roxbury, it was unclear how many children would be attending.

“We’re getting a lot of parent dropoffs. That’s all we know,” said one person who declined to identify herself and was answering phones, shortly before the 8:30 a.m. start time at the elementary school.

Another woman, who also declined to give her name, said “some parents don’t even know about” the strike and had been calling, wondering where their buses were.

The strike also affected Boston charter schools, which use city buses. “We didn’t get one bus today,” said Denise Choukas, an administrator at the Neighborhood House Charter School in Dorchester, which has 400 students, kindergarten through eighth grade.

“A lot of kids got rides in. We’re hoping by the end of the day, [the drivers] will be back to work. Our phone is ringing off the hook.”

The two candidates running for mayor of Boston said they were disgusted by the job action.

“It is shameful for the school bus drivers union to use our children as pawns in a political game,” City Councilor John R. Connolly said. “This is about safety first and foremost, and it is totally unacceptable that our children were put at risk this morning, not to mention the impact on thousands of parents who will miss work. Missing even one day of school is a real problem for our children who face a daunting achievement gap.”

Representative Martin J. Walsh said, “Kids and parents must come first. This is wrong. The bus drivers have put our children in harm’s way. This is an illegal action, causing a huge disruption, and I call on the bus drivers to return to work immediately. This is a violation of the contract and cannot be tolerated.”

The last time city school bus drivers went on strike was in 1991, according to news archives.