The woman, who was treated for smoke inhalation and minor cuts, said she also wanted to thank friends and neighbours who had come to her assistance.
She said the speed of the fire had "overwhelmed her".
"I was just turning the electric blanket off and I flicked the control and it ignited in my hand. I hurried into the bathroom and put a towel in some water to try and douse the flames but by the time I got back it had already spread too far. The whole bed was alight."
Mr Oldham was driving past on a patrol when he saw the single-storey Maranui St home engulfed in flames about 6.45pm on Sunday.
He made several attempts to get into the building and smashed his way in through a window. It then took him two attempts to get the woman from the blaze and he couldn't have done it without help from fellow police officer Mr McCarthy.
Two sets of neighbours told the Bay of Plenty Times they were amazed the woman was alive.
Anahere Harper and Daniel McLeod have lived next to the victim for two years and said the fire was so fierce their front fence glowed "orange" and a tree on their property caught alight. "Moments after I walked outside to see what was happening there was an almighty woosh," Miss Harper said.
They tried to put the fire out with a garden hose before the fire crews arrived, but were forced to flee to the roadside because the heat was too intense.
"She's a very, lovely lady, and so, so lucky to be alive. It makes me almost cry thinking about it," she said.
Stunned neighbours Jan and Gerald Connery, who have lived next door to the woman for about 10 years, said they were extremely upset for the victim.
Mrs Connery said she was cooking dinner when she heard loud banging, which must have been the cladding on the house exploding.
"When I looked out I saw flames coming out of the window as high as the roof. I got quite a shock actually. I was so relieved when I saw the police were bringing her out," she said.
"We were told by police to prepare to evacuate if needed but luckily it did not come to that. It is so fortunate the police officer was driving past."
One of the victim's two daughters said her mother was discharged from hospital yesterday and was "doing okay considering".
Her mother, who had lived at the property for 26 years, would be staying with her in Greerton until the family had a chance to discuss what to do next, she said.
"I want to say a huge thank you to all the emergency services and police staff for everything they did.
"They were absolutely amazing.
"I have always said everything you own can be replaced but you can't replace a life and I'm so grateful my mother is alive," she said.
The daughter said the house was insured and had working smoke alarms.
Western Bay of Plenty area commander Inspector Clifford Paxton and Police Commissioner Mike Bush have praised the men's actions.
