Expressing grief over the accident, Uttarakhand Chief Minister Vijay Bahuguna ordered a magisterial inquiry into it and announced compensation for the families of the victims.
The accident occurred when the bus, carrying 47 passengers, was coming to Vikasnagar from Hanol.
The vehicle skidded off the road and fell into the ditch, said Dehra Dun District Magistrate Ravinath Raman.
Search and rescue operation has been launched and 18 bodies have so far been recovered from the ditch, he said.
The dead included six women and a child.
The injured are being rushed to various hospitals of the area, Raman said.
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The cause of the accident was not immediately known, he said.
Announcing an ex-gratia of Rs one lakh each to the next of kin of those killed and Rs 50,000 to those seriously injured, the Chief Minister has directed the district administration to provide best medical care to those injured.