The injured were rushed to regional hospital Bilaspur where they were out of danger, the police said.
The ill-fated bus was on its way to Manali.
Chief Minister, Thakur Sukhvinder Singh Sukhu and Deputy Chief Minister, Mukesh Agnihotri has expressed grief over the death of a girl from Jaipur.
Chief Minister directed the district administration to provide immediate relief to the next of the kin of the deceased and best medical treatment to the injured.
The police is probing the cause of accident and have started the inquest proceedings in the case.