An instructor for a private operator about to take over public bus services in Sydney's inner west has been hit and killed during a training exercise, leaving colleagues in a "state of shock".

The incident happened in a vacant car park in Smithfield just before 10:00am.

Both the trainee driver and the instructor were employed by Transit Systems, which won a State Government tender to run services in Sydney's west from July.

Police are investigating the circumstances that led to the government bus ploughing into the instructor, who died at the scene.

"It was a very tragic accident," NSW Police Assistant Commissioner Michael Corboy said.

"It's a good reminder for pedestrians to keep a lookout especially around buses."

Police Minister Troy Grant said the accident was "a stark reminder of how quickly a life can be taken for pedestrians".

"It is a tragic situation that the crash investigation unit will get to the bottom of to give answers … to the families that have been devastated by [Thursday] morning's event."

Transit Systems released a statement saying it was cooperating with the investigation.

"It's with great sadness that I report one of our trainers was involved in an accident [on Thursday] morning while taking part in a routine training session," Transit System's chief executive Clint Feuerherdt said.

"We are in a state of shock and grief and our sympathies are with the family of the trainer, who was much respected by his colleagues."

The Berejiklian Government's decision to privatise the inner west bus services was controversial.

Last year, about 1,200 government bus drivers walked off the job in protest.

The Government went ahead and awarded the tender to Transit Systems in February.

Transit systems currently operates bus services in Parramatta, Fairfield and Liverpool.