Nar Bahadur Darlami, 35, and Yubaraj Gurung, 22, both from Surkhet, died in the accident, the Area Police Office Kohalpur said.
Those injured are being treated at the Kohalpur Hospital. The bus was heading to Surkhet from Nepalgunj.
Tharu and Magahi speakers, along with their supporters, protested in front of the provincial assembly, calling for the bill's withdrawal and the inclusion of the Tharu language.