The number 50 service went up in flames near St James’s Hospital on Beckett Street, Burmantofts, shortly before 9am today.
It is believed the driver had pulled up after being alerted to smoke coming from behind his seat.
A spokesman for First bus company said: “We would like to praise the driver, whose quick thinking meant he was able to immediately get passengers off the bus and tackle the blaze before alerting the emergency services.”
The road was closed while firefighters from Gipton dealt with the incident.
Watch commander Matthew Walsh said: “There was very thick smoke when we got there.
“The bus was quite badly damaged. Where the driver sits was totally burned out. It spread up into the upstairs above the driver’s seat and the entire bus was smoke-logged.”
Crews were at the scene for about an hour.
An ambulance was called to the scene but nobody was hurt.
The cause of the fire is under investigation by First, which also organised recovery of the bus.