The bus veered off Prithvi Highway on Friday and rolled toward a fast-flowing river, stopping on the rocky bank.
The top part of the bus was ripped, but the wreckage did not plunge into the Marsyangdi River.
Armed Police Force spokesperson Shailendra Thapa said that, among those pulled out of from the bus, 14 were declared dead and 16 were injured in the accident.
Officials could not yet say how many more were missing or the exact number of people on the bus when it crashed, but they estimated there were some four dozen on board at the time of the accident.
Police and army rescuers were helping to pull people from the wreckage near Abukhaireni, a town about 120km west of the capital, Kathmandu.
The bus from neighbouring Indian town of Gorakhpur was heading toward Kathmandu from the resort town of Pokhara on Friday when it drove off the highway midway in the journey.
In July, two buses were swept by landslides not too far from Friday's accident site.
Of the 65 people on board those two buses, only three survived and only about half the bodies were recovered.
The wreckage of those buses have not been found yet but authorities have continued to search.
Bus accidents in Nepal are mostly due to poorly maintained roads and vehicles and much of the country is covered by mountains with narrow roads.
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