The driver fled and a manhunt was underway after the tragedy in Uttar Pradesh state, media reports said.
The dead — four women and three children — were among pilgrims planning to take part in an early-morning dip in the Ganges, which is considered sacred by Hindus.
“As it was still dark when they arrived, many people decided to sleep along the road until daybreak,” police superintendent Santosh Kumar Singh told AFP.
“At about 4 am another bus carrying pilgrims reached the site. There was a bend and the driver probably didn’t anticipate people sleeping so close to the road.
“When he took the turn, the four women and children were caught under the wheels,” the police officer said.
More than 150,000 people a year are killed on India’s roads, which are considered among the most dangerous in the world.
The deaths are often blamed on speeding drivers, bad roads and poor law enforcement.