The incident happened at Bulbulchandi village around 7 am when the girl, a class seven student was going to school.
The Malda-bound killer bus fled the scene, but angry villagers damaged two other private buses, police said.
Officers from Habibpur police station reached the spot with a force but could not control the situation.
Later, the combat force had to be deployed to bring the situation under control.
"Accidents occur regularly at this place and we are talking to the police to find a solution," BDO Of Habibpur Phurba Dorjee Sherpa said.