The bus, carrying over 30 pilgrims from Vaishali district in Bihar, was on a tour of religious places in the region and had arrived at Tarapith Kali temple only yesterday from Deoghar's Basukinath temple in neighbouring Jharkhand, Burdwan Superintendent of Police S M H Mirza said.
The accident spot was not very far away from Burdwan district.
The 11 injured were being treated at Burdwan Medical College and Hospital where the condition of some was stated to be critical, Mirza said.
The SP said the driver probably lost control and the vehicle overturned twice as local people started rescue operation soon afterwards alerted by the screams.
Other injured passengers of the bus were being treated at Dhaniakhali Rural Hospital.