The accident occurred at 7 a.m. in Hansapur, a village in the Arghakhachi district 300 kilometers southwest of Kathmandu, district chief administrator Balbhadra Giri said.
"Twelve bodies have been recovered. A search operation continues because we believe there are more bodies," Giri said.
Thirty-one people were aboard the bus. According to preliminary reports, the accident was caused by the poor condition of the road.
Traffic accidents are common in Nepal's hilly districts where roads are poorly maintained and have sharp turns.