Public servant Lauren O'Neill, 29, was badly wounded after being bitten on the leg while swimming near a jetty at Elizabeth Bay, in the city's eastern suburbs, at dusk on Monday.
It was the first serious attack inside the harbour since 2009 when navy diver Paul de Gelder lost his right leg and hand to a bull shark.
In 1963 actress Marcia Hathaway was also attacked by a bull shark while wading at Middle Harbour and later died.
Sydney University shark policy expert Christopher Pepin-Neff said humans were an unfamiliar sight for the predators and could provoke the animals' fight-or-flight response.
"Sharks do not know what humans are, we are a very large land animal swimming through the ocean," he said.
A vet who rushed to the scene and stemmed the bleeding has been lauded for saving Ms O'Neill's life. (Dan Himbrechts/AAP PHOTOS)
The main method of sharks engaging with their environment is using their teeth, which can lead them to bite unfamiliar creatures.
"Bull sharks are biters, if you get in the way of a bull shark and it doesn't know what you are, it is going to bite," Dr Pepin-Neff said.
Ms O'Neill was saved after neighbour Michael Porter heard faint yells for help through his open window.
"It was absolutely mortifying, horrifying, I've never experienced anything like it," he told Nine's Today program on Tuesday.
He ran to help and was quickly joined by several others, including a vet named Fiona who applied tourniquets to stem the bleeding and has been hailed as a hero.
Ms O'Neill's significant wounds meant there blood was everywhere and, while in little pain, she struggled to maintain consciousness before paramedics arrived, Mr Porter said.
She was rushed to nearby St Vincent's Hospital for surgery.
Ms O'Neill was in a stable condition in the hospital's intensive care ward on Tuesday afternoon.
"Fiona is a hero and I believe she saved her life," Mr Porter said.
"I'm not sure what would have happened (without her) but it wouldn't have been good."
The vet was also lauded by Deputy Premier Prue Car as a "legend" and Health Minister Ryan Park.
Mr Park thanked first responders and hospital staff.
The beach-focused SharkSmart alert system has detected and tagged eight bull sharks off Sydney's beaches in the past week.
"Our research has highlighted that individual bull sharks are constantly moving throughout the harbour and there is no evidence of any territorial behaviour by individuals," Agriculture Minister Tara Moriarty said.
"Research has also shown that bull sharks are especially numerous when water temperature is around 22C, which is close to the average water temperature across Sydney at the moment."
The sharks make the journey to Sydney from Queensland every summer to hunt for fish.
People should take extra care of sharks when in murky, dirty water, such as after high rainfall or floods, where there are lots of baitfish and diving birds around and when within one kilometre of a river, the NSW government advises.
Dr Pepin-Neff said swimmers should be mindful in warm water and stick to fully enclosed harbour beaches when possible.
"People talk about dawn and dusk as a bad idea but most shark bites happen between 12 and 2pm because that's when the most people are in the water," he said.
"I realise that it's asking the impossible in a scorching summer."
No shark-related deaths have occurred in Sydney Harbour since 1963 but a 35-year-old man was killed by a great white shark while swimming at Little Bay beach in Sydney's east in 2022.
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