The incident occured at the corner of Gorgie Road and Robertson Avenue shortly before 11am.
The driver and passengers were forced to get off the vehicle, operated by First Bus.
Two appliances from Tollcross Fire Station attendend the scene.
A spokesperson for Scottish Fire and Rescue Service (SFRS) said no passegers were injured in the incident.
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The fire was quickly extinguished and the road reopened.
An SFRS spokesperson added: "We received a call at 10:51am regarding a bus on fire on Gorgie Road near to the Tynecastle football stadium.
"Two appliances were dispatched from Tollcross Fire Station and the fire was extinguished.
"Crews remain on site to make sure the area is safe."