The day before the start of New York City’s first school bus strike in 34 years, a long yellow bus pulled up at Public School 282 in Park Slope, Brooklyn, and the little bodies that popped out could be counted on one hand: Three. The big bus had dropped off part of its cargo earlier, at another school, but in all, 10 children had ridden on a bus fit for about 60.

A similarly large bus pulled up with 17. Finally, a modern-looking bus whose side panel said it could carry 66 children arrived with its passengers: Five children.

“I think in some cases, we have one child on the bus,” said Kathleen Grimm, the city’s deputy schools chancellor for operations.

The strike that began Wednesday, which idled more than half of the city’s school buses and forced about 113,000 children to find new ways to school, was prompted by a fight over union jobs. But its true roots are in an attempt to reform one of the most inefficient transportation systems in the country, one that costs almost $7,000 a year for each passenger, an amount so high that many of those children could hire a livery cab for about the same price. By comparison with the next three largest school districts, Los Angeles spends about $3,200, Chicago about $5,000, and Miami, $1,000.