The three were among 52 passengers in a bus bound for Nairobi, which crashed at the Minduka centre.
Busia police boss Kenneth Kimani told journalists that the incident occurred when the driver of the bus lost control over the vehicle while overtaking.
“The death toll is at three; ten people have been admitted to hospital but 30 others have been treated and discharged,” he said.
Kimani narrated that the accident occurred at Minduka centre in the outskirts of Busia town just after the bus left for Nairobi.
The OCPD made a passionate appeal to drivers to be cautious on the roads at this time when they will be particularly busy as people travel for Christmas.
Police have promised to be on high alert this season, to avert deaths on the roads that are usually at their highest at the end of the year.
Officers will be clamping down on drunk driving, errant driving and un-roadworthy vehicles in the Christmas and New Year period.