The incident happened on Thorner Road at about 11am on Tuesday morning on a service from Harrogate to Leeds.
Footage on social media shows the back of the bus up in flames while passengers escaped the fire.
Crews from Killingbeck and Wetherby were called to put out the fire and remained at the scene for over an hour.
There were no reported injuries.
A spokesperson for West Yorkshire Fire said: "We were called at 11.12am to reports of a bus on fire on Thorner Road in Bramham.
"Pumps were sent from Killingbeck and Wetherby.
"Officers left by scene by 12.09 and there were no reported injuries."