11 passengers were admitted to a local hospital where two were stated to be critical, police and officials said.
The bus proceeding from Sakleshpur to Belur had several students on board, police said. There were reports that the bus was carrying 50-60 passengers.
Karnataka Transport Minister Ramalinga Reddy said according to his information the bus had about 50 passengers.
Eight bodies have been pulled out of the lake, where the water storage level was low and the silt had accumulated, they said, adding fire brigade, police and local fishermen, were engaged in relief operations.
He said the driver and conductor survived the mishap.
Hundreds of onlookers gathered around the lake, impeding rescue and relief operations.