Police said the students of St Mary's Nyamagwa Girls Secondary School went on a road trip to celebrate the purchase of the bus the day before.
The 52-seater vehicle which had 78 students overturned in Rioma area while they headed back to school.
Ondari Otieno, CEO of Kisii Teaching and Referral Hospital Hospital, confirmed the deaths of the three and said five students were in critical condition.
The five were to undergo surgery, he said, and added that 68 students were taken to the hospital with injuries.
A witness said some of the students had deep cuts on their heads.
"The driver of the bus also seemed to be new. It is said he had driven the bus from Nairobi on Thursday night," the witness added.
The NTSA said in a statement that the bus, operating on KG plate number 6375, was being driven by an Associated Motors driver.
"The bus which was driven by Erick Gituma is reported to have been overloaded and speeding when it rolled several times while negotiating a sharp corner," said director general Francis Meja.
The accident comes barely two days after one pupil died and seven were injured after their school on Lang'ata road in Nairobi.