The incident happened within the grounds of the city's bus station in Smithfield Street just before 10:30 GMT on Monday.
The woman was in her 30s but her name has not yet been released.
The depot is now closed. Translink confirmed that an incident had taken place and that an investigation was under way.
An eyewitness at the bus station, Jo-anna McLucas, described what she saw in the immediate aftermath of the collision.
"I was on the phone and I heard a bang, I looked up to see what had happened," Ms McLucas said.
"The bus had hit the wall and I walked outside and there was a small gap between the wall and the bus and I could see there was someone on the ground."
Ciaran Rogan from Translink told the BBC: "Our thoughts and our sympathies are with the family and relations and friends of the young lady involved.
"It really is a tragedy."
Mr Rogan said the bus driver was "distressed" and would be given support by the transport company.
"We would have assistance available within Translink [for those] who are involved in accidents because it can affect people very badly at times.
"We'll give the driver every assistance as we will any member of staff who was badly affected."
Mr Rogan said other Translink workers at the station would be affected by the fatality but added that "our main job at the moment is to find out what happened".

However, researchers at the University of Bristol believe the shape of beer glasses affects the speed people drink.
Their study, published in the journal PLoS ONE, suggests people drink more quickly out of curved glasses than straight ones.
They argue that the curvy glassware makes pacing yourself a much greater challenge.
A group of 159 men and women were filmed drinking either soft drinks or beer as part of the study. The glasses all contained around half a pint of liquid, but some of the glasses were straight while others were very curved.
There was no difference in the drinking time for soft drinks. People drinking from both straight and curved glasses finished after around seven minutes.
However, for the beer drinkers there was a large difference between the two groups. While it took around seven minutes for people drinking from a curved glass to polish off their half pint, it took 11 minutes for those drinking from a straight glass.
The report said: "Drinking time is slowed by almost 60% when an alcoholic beverage is presented in a straight glass compared with a curved glass."
The researchers thought that curvy glasses made it harder to pace drinking because judging how much was in the glass became more difficult owing to its curved shape.
The group of drinkers was shown a variety of pictures of partially-filled beer glasses and asked to say whether they were more or less than half full.
The team said people were more likely to get the answer wrong when assessing the amount of liquid in curved glasses.
The lead researcher Dr Angela Attwood told the BBC: "They are unable to judge how quickly they are drinking so cannot pace themselves."
She suggested that people were not concerned about pacing themselves with soft drinks, which could explain why glass shape had no effect on them.
However, the study looked only at the time taken to finish one drink in a laboratory setting. So it is not certain what happens on an evening out if multiple drinks are consumed.
She said altering the glasses used in pubs could "nudge" people to drink more healthily by "giving control back".
The shape of a glass has already been shown to affect how much alcohol people pour. A study in 2005 showed people were more likely to pour extra alcohol into short, wide glasses than tall, narrow ones.

The Gills had agreed to sign defender N'Gala, 27, after he left Eastleigh.
However, he played for Barnet and Eastleigh earlier this campaign, and rules state a player cannot appear for more than two teams in one season.
But National League club Dover say they have been allowed to sign him following talks with the Football Association and English Football League.
N'Gala started his career at West Ham, and had spells at Stevenage and Portsmouth before joining Barnet in 2014.
He became Eastleigh's record signing when they bought him from the Bees in November.
The Fifa Players' Transfer rules came into force this season, and recently led to Leyton Orient winger Ulrich Nnomo's proposed move to Paris FC being cancelled.
Find all the latest football transfers on our dedicated page.
A woman has died after being knocked down by a bus in Lisburn, County Antrim.
[NEXT_CONCEPT]
The shape of your glass is probably the last thing on your mind when you are down the pub.
[NEXT_CONCEPT]
Bondz N'Gala has joined Dover, a week after a move to Gillingham fell through because of Fifa regulations.