Three of the bodies have been identified as that of Sukmaria Devi (50), Meera Devi (20), Budhni Devi (55), the Deputy Superintendent of Police (DSP) Lalit Mohan Sharma said.
All four victims hailed from Darbhanga district and had gone to participate in Malmas fair at Rajgir, he said.
The cause of death the victims was not known, Sharma said.
The police has seized the bus for the purpose of investigation, the DSP said.