It was a case of a double-tragedy and a miracle for a mother and her two children.

A 38-year-old woman who was carrying her baby in her arms died after getting hit by a bus with her elder daughter on board Wednesday in Sydney.

The woman's 11-month-old baby was hurled away from her arms by the force of the crash, but the baby miraculously escaped serious injuries, even as the woman died at the scene.

The woman was hit at the intersection of Hannah and Beecroft Roads in Beecroft just after 3:00 pm local time on Wednesday.

"The 11-year-old daughter of the deceased lady, the mother, was on the bus with other school children," police duty officer Darren Jameson narrated to Macquarie Radio on Thursday, adding, "It's a tragic day, not only for the family but for the witnesses and the bystanders."

The elder daughter did not see the crash, the police added.

The bus that had struck the woman was carrying students from Beecroft Primary School. The students were returning from an excursion, AAP reported.

The bus driver, 69 years old, has spoken to the police. He went for mandatory blood and urine tests, as police continues its investigation.

Meanwhile, the students on board the bus have started to undergo counseling, to overcome their fright over the tragedy.

Investigators are encouraging witnesses to come forward as they continue to piece the stories together to find out how the woman got in the bus' way on that ill-fated afternoon.

The bus has been taken in by police for forensic examinations.