Mr Vine was riding his bicycle in Kensington, west London, on 26 August when a row occurred, Hammersmith Magistrates' Court was told.
Shanique Pearson, 22, from Vauxhall, is said to have formed the shape of a weapon with her fingers and "cocked it" at Mr Vine's head.
Ms Pearson denies acting in a threatening manner.
In response to the charges she denies using threatening, abusive or insulting words or behaviour and driving without reasonable consideration for other road users.
Ms Pearson has admitted driving an unlicensed vehicle on the day in question.
The defendant claimed Mr Vine was mistaken in what he thought he had seen and said she instead raised her middle finger at the presenter, who she thought was "a bit crazy" for following her after their initial row.
Footage of the argument, which took place in Hornton Street, west London and was filmed on Mr Vine's helmet camera, has since been viewed online millions of times, the presenter said.
The video was played in court.
After initially clashing when Mr Vine stopped his bike in front of Ms Pearson's Vauxhall Corsa, Ms Pearson drove past the Radio Two presenter, the court learned.
But the argument erupted a short while later when Ms Pearson spotted Mr Vine trying to take a photograph.
Explaining the next few moments to the court, he said: "She's gone back in the car, she's sitting at this junction. I am behind her with my cycle, the lights are red. I draw parallel to the car because I want to see inside.
"As I draw level and I look in [to the car] she produces her fingers like this, and aims them at me, and cocks her thumb and goes like that, in a firing sign."
In her evidence, Ms Pearson said she had initially reacted to Mr Vine's stopping in front of her car because: "It was too quick, it kind of shocked me.
"I could have hit him [with the car] and I don't think he understood the danger of that, hence why I was so angry."
The hearing has been adjourned until 26 January.
A driver "made a gun sign" at BBC presenter Jeremy Vine during an alleged road rage incident, a court heard.