According to police, the incident took place around 7 a.m in Aklera area of the district, some 350 km from Jaipur.
"At least 30 of the passengers in the private bus were school children from various villages and were on their way to Bhaatla village," a police officer said.
The bus suddenly lost balance on a slope and overturned, the officer said.
Four school children, identified as Phoolchand, 10, Rajesh Kumar, 9, Rajendra, 12 and Karan Singh, 14 and a helper in the bus Israil, 30, were killed in the accident.
"Over 24 others - most of them school children - sustained injuries. They were rushed to a hospital in Jhalawar where they are undergoing treatment," said the officer.