The driver fled from the spot and police are on the lookout for him, they added.
The incident was reported around 6 am today.
When the bus reached Bakhtawarpur area in Alipur, it overturned, apparently due to a malfunction, said a senior police officer.
The bus was carrying 50 people and water motors were kept on its roof. It is suspected that the bus was overloaded, he said.
Satnaam Singh (56) suffered serious injuries, but he is out of danger, the officer said.