Most of the victims are reported to be schoolchildren, according to local reports.
The bus completely submerged after falling into VC canal at Kanakanamaradi of Pandavapura taluka, they said, adding bodies of 23 victims was fished out.
Among the confirmed dead are a woman and a small child.
At least 24 people died near Kanagana Maradi in Pandavpura Taluka of Mandya district, about 90 km from Bengaluru, after a private bus plunged into a canal.
Mandya is 105km from the city of Bengalaru, located south of the country.
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Locals used rope to try to pull the bus out from the water and into a field.
The sources said the bus skidded around 60ft from the road before coming to rest on its left side on the canal bed, blocking the two doors and reducing any chance of escape for the trapped passengers. The driver of the bus lost control after colliding with a buffalo and plunged off the bridge into Mahanadi river bed, an eyewitness said. "I will find out, take some more inputs". My thoughts are with the families of the deceased.
Kumaraswamy has ordered the suspension of Mandya road transport officers responsible for ensuring that local buses meet all fitness parameters.
He has also said his government will postpone the state cinema award ceremony that was scheduled to be held this evening. "I extend my deepest condolences to the families of the deceased & pray for the speedy recovery of the injured", Congress president Rahul Gandhi wrote.
Police officials have reached the spot and relief, rescue work was underway.