The double-decker vehicle hit the brick wall of the Quorum offices on Old Market last night (June 11).
One witness described how the bus “demolished” a traffic light before slamming into the front of the building.
First Bus has now confirmed the driver of the bus was taken to hospital but received no major injuries.
The company added no passengers were on board and it is investigating the incident.
Ian Coyle, operations director for Bristol at First West of England, said: “A bus running out of service to the depot was involved in an incident at the Old Market roundabout yesterday evening causing it to leave the road and come in to contact with the Quorum office building.
“No one was injured in the incident and there were no passengers on board our bus.
“The emergency services attended the scene and our driver was taken to hospital with no major injuries.
“We worked with the police and fire brigade yesterday evening to secure the site and safely remove the bus from the scene.
“The safety and well-being of our passengers, drivers and the public are our number one priority and we are conducting a full investigation to determine how this incident happened.”