The 49-year-old, who cannot be identified for legal reasons, pleaded guilty to attempting to take a child and common assault, over the incident in December 2022.
She was sentenced on Wednesday at Sydney's Downing Centre District Court to a maximum sentence of three-and-a-half years in prison.
The woman will be eligible for parole on March 29, 2025.
She approached a nine-year-old girl and her grandmother while they were waiting at a bus stop in Sydney's southwest, grabbing the girl by the arm and saying: "Come with me."
The girl's grandmother asked what she was doing, telling her to stop and get away.
"That's my daughter," the woman replied.
During the attempted abduction, the child was screaming to her grandmother: "Nanny, stop her, stop her!"
The woman swung at the grandmother in a struggle that lasted roughly a minute, poking her in the eye and causing redness and swelling.
The grandmother was able to break the woman's hold on the child, after which the would-be abductor said: "I'm going to kill you."
The woman fled into a nearby unit complex but was later tracked down by police.
When she was arrested, the woman appeared to be agitated and "highly intoxicated", and had a bag of children's toys, the court was told.
Judge David Wilson described the incident as highly traumatic for those involved as he sentenced the woman and placed her on the child-protection register.
"The attempt to take a child away from parental control is a serious offence," he said.
He noted the woman had a long history of drug use and at the time of the offending was not taking medication, including prescribed anti-psychotics.
Judge Wilson found the woman was remorseful of her actions and that her moral culpability for the crimes was reduced because of her "substantial, long-standing and ongoing" substance abuse.
He ordered the woman to be referred to drug and alcohol and mental health services on her release.
"You've had a rough time but you've also inflicted a lot of harm on the community," Judge Wilson told the woman.
"Can you please take this as an opportunity to turn your life around?"
"Yes, sir," she replied.
The woman was previously jailed for manslaughter after placing her daughter in a scalding hot bath, causing serious burns to around 75 per cent of the baby's body in 2003.
She later left the unit with the baby in a stroller, attempted to buy drugs and arranged with a passing motorist to perform a sex act in exchange for money.
Police later found the woman and her dead child.
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