The demonstration of the prototype in Glasgow comes ahead of the planned launch of passenger services across the Forth Road Bridge late next year.
Trials without passengers over the crossing are planned by the end of this year.
The single-decker was driven round a cordoned-off section of the SEC car park in Glasgow as part of the CAV (Connected and Autonomous Vehicles) Scotland trade show.
It is being developed in the joint Project CAVForth project between Stagecoach, bus maker Alexander Dennis, Transport Scotland and tech firm Fusion Processing.
Bristol Robotics Laboratory and Edinburgh Napier University are also involved.
A fleet of five buses is expected to start carrying passengers on a 14-mile route over the bridge between the Ferrytoll park and ride site in Fife and Edinburgh Park tram/train interchange from late 2020.
A driver will remain on board the 42-passenger buses for safety.
Extensive trials have already taken place at a Stagecoach bus depot in Manchester.
Stagecoach Scotland East project manager Louise Simpson said: "We are doing a lot of research with passengers.
"We hope they will be excited. We understand that some may be sceptical and slightly fearful of the new technology, but that's nothing new in the advancements in technology in general.
"But I don't think in the near future there will be buses running without a driver on board on public roads.
"Safety is the key advantage - autonomous technology can act as quite a significant support for the driver and help remove a lot of human error that is a factor in collisions."
Transport Secretary Michael Matheson said: “I was particularly pleased to experience the demo of the prototype automated bus system as it’s the type of innovation that shows Scotland is very much open for business when it comes to trialling these types of vehicles.
“Our trunk road network can provide a wide range of environments as a diverse testing ground, and the ground-breaking and globally significant Project CAVForth will really help Scotland establish its credentials on the world stage.”
Stagecoach Group chief executive Martin Griffiths said: “We are very pleased to be leading the way in Scotland’s first autonomous bus trial.
“Our industry, customers and employees can benefit hugely from autonomous technology as it can make services safer, more efficient and help to deliver better journeys.
"We’re also investing heavily in the skills and development of our people.
"Alongside new technology developments, our employees will continue to play a critical role in delivering sustainable mobility services that our customers trust and rely on.”
Jim Hutchinson, chief executive of Fusion Processing, said: “CAVForth is the most advanced autonomous Bus project we see anywhere to day.
"As well as providing autonomous systems, Fusion Processing will provide spin-off projects from the technology that can help today’s manual driven buses, such as tech that can recognise pedestrians and cyclists and warn the driver, automated emergency braking, and replacement of external mirrors with advanced vision systems.”
Alexander Dennis chief executive Colin Robertson said: “We are at the forefront of innovation in the bus industry.
"This trial allows us to evaluate potential benefits of autonomous technology under real operating conditions, and feeds into our extensive work to further improve the safety of buses with the help of state-of-the-art technology.”