The private bus was one of eight hired to take Haridwar city traders on a picnic in Mussoorie, a popular tourist town surrounded by green hills and snowy mountain ranges about 20 miles (30 kilometers) from the state capital, Dehradun.
The bus was carrying 52 people back to Haridwar late Wednesday when it flipped over at a curve in the road and rolled down the gorge, landing upside down, Tamta said.
Using ropes and a ladder to climb down into the gorge, local villagers and government rescue officials worked for hours to bring the injured and the dead back up to the road.
The driver, who initially fled the scene, was arrested Thursday, Tamta said. A witness told officials that several passengers had asked the driver to slow down before the accident, he said.
Shops in Haridwar were closed Thursday as the city mourned the dead.
Uttarakhand Chief Minister Ramesh Pokheriyal visited the injured at Dehradun's hospital and pledged to give each 50,000 rupees ($1,000). He said the families of those killed would receive twice that amount.
Mussoorie, also known as Queen of the Hills, sits at an altitude of 6,170 feet (1,880 meters).
Road accidents are common in India, which has the world's highest annual road death toll, according to the World Health Organization.
More than 110,000 people die each year across the country in traffic accidents caused by speeding, bad roads, overcrowding and poor vehicle maintenance, according to police.