Local television footage showed rescue workers in waist deep water pulling bodies from the bus, which was half submerged in the river Banas some 160 kilometres (100 miles) from the state capital Jaipur.
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"We have retrieved 32 bodies from the bus and shifted the injured to the hospital," district magistrate Kailash Chand Verma told AFP.
He said emergency workers equipped with steel cutters rushed to the scene of the accident to rescue those trapped inside the bus.
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Authorities had yet to confirm the cause of the crash, but survivors said the driver lost control while trying to overtake another vehicle.
India has some of the world's deadliest roads. More than 150,000 people are killed each year with most accidents blamed on poor roads, badly maintained vehicles and reckless driving.
Rajasthan, known as the desert state, is popular with both international and domestic tourists drawn to its palaces and desert forts.
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