The incident happened around 4.25pm on Tuesday on the A71.
A rust or gold coloured old style saloon car leaving the Lizzie Brice roundabout lost control and crossed into the path of a double-decker bus and a Ford Fiesta, which were travelling east.
After colliding with both vehicles the driver made off from the scene and was last seen heading northwards along the A899 Livingston road.
The westbound carriageway of the A71 was closed for around one hour while police dealt with the incident and carried out an investigation.
Both the bus driver and the driver of the Fiesta suffered minor injuries but did not require medical attention.
Officers are now keen to trace the motorist who left before they arrived and would urge anyone who can assist with their enquiries to come forward.