Boston school buses rolled throughout the city today, as officials grapple with the fallout from the one-day surprise drivers strike on Tuesday.

“It went as well as could be expected,” Brian Ballou, a School Department spokesman, said of this morning’s bus runs. “We know things are heading in the right direction.”

Afternoon bus service is running smoothly.

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The bus drivers union and Veolia Corp., the private contractor that oversees the city’s four bus yards and its bus fleet, are still sorting through a myriad of issues, many dealing with pay and benefits. It remains unclear when the issues will be resolved.

Buses this morning ran at their best rates since Tuesday’s strike, with 95 percent arriving on time and 99 percent arriving within 10 minutes, Ballou said.

A notable milestone in the talks could come Thursday when both sides plan to meet again to evaluate their progress and discuss where they stand on the specific concerns raised by the union.

The Charlestown bus yard experienced a slight delay in service this morning when one individual blocked two buses from leaving by briefly standing in front of the exit.

“This is the third day in a row that a very small group of individuals has attempted to disrupt service and the third day in a row that the vast majority of drivers have ignored them,” Ballou said.

With service running smoothly for the most part for three consecutive days, school officials are evaluating whether they will need to keep contingency plans in place when school resumes Tuesday after Columbus Day. A critical part of those plans has been opening schools an hour early to accommodate parents commuting to work. Many parents are still hesitant about placing children on buses in light of the Tuesday strike.

Any changes to the contingency plan will be posted on the School Department’s website prior to Tuesday.

Parents can use the “Where’s My School Bus” app at schoolbus.bostonpublicschools.org to check the status of their bus, or call the Transportation Hotline at (617) 635-9520 or the Mayor’s 24-Hour-Hotline at (617) 635-4500 for more information.

The union has raised myriad issues, which center on pay, benefits, and respect.

In particular, the union is trying to persuade the company to stop using GPS data and a bus-routing software program to calculate how much time it should take drivers to do a route, then using that data to determine their “flat” pay rate. The union contends that the practice is forbidden under its contract. Drivers have said the computerized data tends to underestimate travel times in heavy traffic, ultimately shortchanging them on pay.

Similarly, the union is asking for restoration of what they call a contractually mandated daily school bus report, in which drivers record the time it takes to perform all their duties, such as cleaning up their buses at the end of a shift, which can be time consuming.

The union also has accused Veolia officials of refusing to meet with them on many occasions since the company assumed oversight of the city’s four bus yards in July. Consequently, the union filed a complaint with the National Labor Relations Board in August, outlining its grievances.