Senior Constable David Mits, 42, had asked the woman what she could offer him after he pulled her over last year, the Melbourne Magistrates Court heard today.
Mits took the woman's mobile phone number and arranged to meet her twice so they could discuss the matter further, the court heard.
The woman recorded the second meeting at which he said sexual favours would be a "bonus" and then reported him to police.
Mits today pleaded guilty to corruptly seeking certain favours from a member of the public as an inducement to act in violation of his official duty as a police officer.
Mits was on a routine patrol on the Mountain Highway at Bayswater, in Melbourne's outer north-east, on January 23, 2007, when he pulled over a Holden sedan, the court heard.
He asked the woman why she was not wearing a seatbelt or displaying P-plates.
The woman, who cannot be named, said in a statement that she told Mits her sister had borrowed the car and removed the P-plates, and she wasn't wearing a seatbelt because she "wasn't thinking".
Mits asked if she had been in trouble with police before, and she told him she had only a couple of points left on her licence due to speeding infringements, she said.
"He said that he didn't really want to give me the tickets and asked me to convince or persuade him otherwise," she said.
Mits phoned the woman at 5pm that same day and arranged to meet her 10 minutes later.
"He asked whether I had thought more about what I could offer him," the woman said in her statement.
"I said that I didn't understand what he was asking.
"He kept asking me the same question."
Mits left the woman to think about the situation and arranged to meet her outside her house at 9pm.
This time the woman recorded their conversation on a digital recorder, the court heard.
Mits told the woman she was "young and good looking" and again asked what she was prepared to do for him, according to documents tendered to the court by the prosecution.
"The victim has asked the defendant if he was asking for sexual favours," the prosecution said.
"The defendant has replied to the victim saying that he was not asking for that if she was not comfortable in offering it, but that it would be a bonus if she did."
The woman then reported the matter to police.
Magistrate Jelena Popovic ordered that Mits, who is currently on bail, appear in the County Court in May.