The mishap took place when the driver lost control of the bus, Lokahi police station in-charge Rajkishore Baitha said.
A person, identified as Bhogi Prasad (23) died on the spot, while 12 others sustained injuries, he said.
The injured were admitted to the nearby Primary Health Centre (PHC) where the attending doctors referred five seriously injured persons to the Darbhanga Medical College and Hospital (DMCH) for treatment, Baitha said.
The minimum was carrying passengers from Jhanjharpur to Lokahi in Madhubani district, he said.