The ill-fated bus was on its way to Ani from Kullu when it skidded off road and rolled down into the river near Jhiri, 20-km from Kullu.
Twelve bodies have been recovered while 15 persons were rescued and rushed to hospital, Deputy Commissioner, Kullu, Sharab Negi, said.
There were more than 50 persons on board the bus at the time of mishap, he said, adding the driver jumped off the vehicle before it plunged into the river.
Relief and rescue teams have reached the spot and efforts are being made to recover the bodies and pull the bus out of the river, the official said.
The bus which toppled up side down after the accident, completely submerged under water and only the tyres were visible, sources said.