The bus from Nepalgunj fell into the Pina Jhyari river in the Chhayanath Rara Municipality, My Republica reported.
"The latest death toll from the accident stands at 32. The number of people injured is rising as we learn more about the situation," the report said.
Many passengers on the bus were returning home from various parts of the country to celebrate the Vijayadashami festival.
A Nepal Army chopper was dispatched from Surkhet to carry out rescue work at the site of the accident.
Santosh Shah, the In-Charge of Nepalgunj Airport Security Guard, said 10 persons who received deep injuries on their head were taken to Kohalpur Medical College and five others were sent to a nursing home in Nepalgunj for treatment.