The injured have been admitted to a local hospital.
Hundreds of Hindu, and some Muslim, devotees from towns in Rajasthan and the neighbouring states of Uttar Pradesh and Madhya Pradesh travel to the Ramdev temple on every Tuesday and Saturday for prayers.
The bus, which was ferrying pilgrims, fell after the driver lost control of the vehicle due to over-speeding.
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At least 32 people were killed Saturday when a bus carrying passengers fell off a bridge into a river in northwestern India, police said. According to sources, the bus broke through the bridge wall and plunged into the Banas River. The exact cause of the accident will be ascertained after an inquiry.
India's roads are notoriously risky.
Rajasthan Chief Minister Vasundhara Raje tweeted to say: "Deeply pained by the accident in Dubi, I had talked to to the officers and asked them to provide assistance to all those who are affect".
PM Modi expressed grief over the incident and said his thoughts were with the families of the deceased. Rescue operations are underway.