Trick or treaters who were in the area on Monday night may hold the key to the crime, they believe.
Castle Hill local area commander Superintendent Phil Flogel said children were trick or treating in Ms Bradbury's street on Monday evening.
"Anybody that visited that particular address, at 45 Kerrie Road, Oatlands, with their children and may have been there in the afternoon as well, directly after school, please contact us.''
Ms Bradbury suffered multiple injuries, and it is understood she may have sustained fatal head wounds.
Westmead Hospital Acting General Manager David Beard said staff were shocked and "deeply saddened'' by the tragedy.
"Lyn was a much loved, respected and long-standing member of the ED team who was always friendly and caring towards patients seeking care at Westmead,'' he said in a statement.
"She will be sadly missed.''
Mr Beard said the sympathies of all Westmead staff went out to her family.
"Our thoughts are with her loved ones during this very difficult time,'' he said.
It is understood the couple lived alone but have adult children.
Police do not know if Ms Bradbury was handing out Halloween treats and wouldn't comment on whether there were any signs of forced entry.
Investigators have not found any weapon in the home and would not comment on whether the victim may have known her attacker.
"It's an area that we respond to from time to time, but generally it is a nice, safe community,'' Supt Flogel said.
Anyone with information is urged to contact Crime Stoppers on 1800 333 000.
- AAP