The drama occurred when a rear wheel of the First- operated bus lurched into the gaping road crater caused by subsidence from a burst water main.
A cordon was put up around the stricken vehicle as it tilted at a precarious angle over a post box outside George House.
No passengers were on board when the bus became stuck but engineers had to assess the situation for hours before using tow trucks to haul the vehicle out.
Eyewitness Billy Murdoch, 60, of Glasgow, said: "They had engineers out taking photos of this - the bus was tilting at quite an angle."
The vehicle had stopped in a bus lane outside the building – used as a set in the Brad Pitt film World War Z during shooting in the summer of 2011 – when it began to sink at about 2.30pm.
Staff from First and Strathclyde Passenger Transport directed pedestrians away from the tilting vehicle.
Glasgow City Council closed the square between North Hanover Street and North Frederick Street from 7pm until the bus was remo-ved. Diversions were in place.
A Scottish Water spokesman said: "The burst on an eight-inch main has caused subsidence on the road.
"Traffic management will be required while we work to repair the burst and reinstate the damaged road. We apologise for the inconvenience.
"The burst has also affected supplies to a very small num- ber of properties in the area."
A police spokesman confirmed no-one was hurt in the incident while a spokesman for First Glasgow said: "It would appear that the vehicle was sitting at the bus stance when the road surface subsided.
"We have yet to assess the damage to the vehicle, but we will be making representations to the local authority about the conditions of roads in the city."
The bus was away by 8.40pm and a council spokesman said: "The Square has reopened but one lane on its north side remains closed for repairs."