Brisbane City Council has apologised to a mother and her son after the pair were told they could not fit on a mid-afternoon bus outside the Queensland Children's Hospital (QCH) in South Brisbane.

Sarah Thomas and her 10-year-old son Lewis Railton were trying to catch a bus at Mater Hill station on Monday afternoon after leaving QCH, where Lewis had undergone a serious medical test.

Lewis had been undergoing a medical test at the hospital. ( Supplied )

Ms Thomas said the bus driver refused to take them on board, claiming her son's wheelchair would not fit.

"The bus pulled up, let some passengers out and the driver said he couldn't take me and tried to drive away but I waved him down and asked him what was happening," Ms Thomas said.

"He said the bus was too full. I got on the bus and had a look — there was room for another 20 people at least.

"I said that if he didn't let my son on I would report him. He shrugged and said again there was nothing he could do, closed the doors and drove away."

Lewis had been undergoing a sleep-deprived electroencephalogram (EEG) at the hospital as part of his treatment for epilepsy caused by a stroke he suffered when he was only three years old.

'Extremely disappointing': Council

Brisbane Deputy Mayor Adrian Schrinner said security vision showed the driver was in the wrong.

"Council has reviewed CCTV footage of this particular incident and we agree that more should have been done to make room on the bus," he said.

He described the incident as "extremely disappointing".

Sarah Thomas said the bus driver told her Lewis's wheelchair would not fit. ( Supplied )

"Council has invested heavily in accessible buses and bus stops to accommodate passengers with a disability," Cr Schrinner said.

"Bus drivers are expected to ask other passengers to make way for wheelchair users so that they can get to their destination safely and quickly.

"Ensuring the city's public transport services are inclusive and accessible is well and truly front of mind for council, and bus drivers receive extensive training about accommodating people in wheelchairs."

Cr Schrinner said the bus driver involved had been counselled and staff have since offered an apology to Ms Thomas and her son.

'Atrocious outside a hospital'

Accessibility advocate Geoff Trappett said the incident is particularly concerning because the station involved is used by hundreds of hospital patients every day.

"It's absolutely atrocious that it happened at that particular location," he said.

"To know that you're picking people up from a hospital area and that they will be using, in most cases, equipment of some kind, you would think that the driver would have had training in that area.

Lewis had just undergone an EEG. ( Supplied )

"The fact the training hasn't sunk in is a terrible, terrible tragedy for all involved, one that should really shake the ground of the transport providers across Queensland."

Ms Thomas said transport authorities needed to take accessibility seriously.

"My hope is that if it does happen again, people do speak up and don't put up with this behaviour," she said.

"It is hard enough living in the disabled world, whether you personally have a disability or you care for someone with a disability. There are so many other things we are faced with that impacts us every day.

"Having something like this really is just another blow that we have to deal with.

"There are kind transport operators out there I know, however the training that they are receiving perhaps needs to have a stronger message."