"We have not been able to pull the wreckage out of the river and believe there are many bodies still trapped inside," police chief Deepak Kumar Thapa told The Associated Press by telephone from the scene of the crash. At least 20 people were still missing, he said.
The bus was full of Buddhist pilgrims on their way to attend a religious fair when it crashed near Bhaluwang town, about 250 miles (400 kilometers) southwest of the capital, Katmandu.
Thapa said the rescue work was suspended overnight and was resuming early Tuesday.
"The people who survived the crash were mostly the ones traveling on the roof. Many of them inside were not lucky to jump out," he said.
Government administrator Tej Poudel said police were still investigating the cause of the accident, but the gravel road it was traveling on was narrow and the bus was overcrowded.
Accidents in Nepal are often caused by poorly maintained roads and overcrowded vehicles. It is common for passengers to travel on roofs of buses.