The incident took place on NH-57 in Narpatganj police station area.
The deceased were yet to be identified, Forbesganj Sub Divisional Police Officer Manoj Kumar said.
The 15 injured passengers were admitted to the Forbesganj Referral Hospital where the condition of three was stated to be critical, he said.
The bus was coming from Forbesganj and heading towards the neighboring district of Supaul.