While 32 people died on the spot, eight injured persons succumbed to injuries on way to hospital.
The bus was on its way to Chamba from Dulera when it plunged into the gorge near Rajera, K C Shadyal, ADGP, Law and Order, said.
The injured have been admitted to hospital.
Rescue operations are in full swing, he said, adding the toll could rise.
Most of the deceased were from Chamba district.
Chief Minister P K Dhumal has expressed grief over the tragedy and directed the local administration to provide relief to the victims.
