The passengers scampered atop the bus in Rajasamud district after it fell into an irrigation stream and settled on its bed, police inspector general Rajiv Dasut said.
"The currents are very strong and the bus could shift so we are rushing two airforce helicopters and soldiers for the rescue," Dasut said from the state capital of Jaipur.
Residents of Rajasamud, 200 kilometres (120 miles) south from Jaipur, said a civilian rescue effort would be risky and added torrential rain was falling on the passengers.
"If that bus shifts, they will all die," a witness said from the site of the accident, located near a highway linking Jaipur and Rajasamud.
Monsoon floods have killed 574 people across India since mid-May and stranded hundreds of thousands.