Smoke was seen billowing from the route 113 double decker as it sat alight outside Finchley Road and Frognal station in the north-west of the capital on Sunday evening.
Footage showed a man using what appeared to be a fire extinguisher attempting to put out flames at the back of the vehicle as others looked on.
One woman, tweeting as Anna, posted a video from the scene and said she heard a bang and screams as people fled.
She said: “Idk (I don’t know) what happened but we only heard a loud bang and then screams and saw people running and then we looked outside and saw the bus on fire.”
London Fire Brigade said they sent two fire engines to the scene at Finchley Road at around 7.25pm and the incident had been dealt with 10 minutes later.
A Transport for London spokeswoman said: “There were no injuries sustained by the passengers or driver and investigations as to the cause of the incident are under way.”