The accident occured when the driver of the bus lost control over the vehicle and hit a road side tree, Purnia Sub-divisional police officer (SDPO) Rajkumar Sah said.
An unidentified woman died on the spot and 15 others were injured in the mishap, the SDPO said.
The bus was on way to Purnia from Madhepura, he said.
The body has been sent to Purnia Sadar Hospital for post-mortem.