The former Australia goalkeeper was charged after he knocked a cyclist off his bike while driving in Sydney's CBD on 21 May last year.
He entered a plea of guilty in the Downing Centre Local Court on Tuesday, after prosecutors agreed to drop the words "furiously" and "dangerous" from the charge.
Police facts tendered to the court say the 43-year-old Fox Sports presenter "turned his steering wheel into the direction of the victim" after the two had a dispute about lane changing on Erskine Street.
Bosnich wound down a window in his black BMW station wagon and told the cyclist: "Champion, you gotta pull a little to the left, you can't keep to the middle of the road."
He then drove past the bike rider but when he had to slow down due to traffic, according to the facts, the cyclist threw an object at the passenger side mirror of Bosnich's car.
"At this stage the accused has turned his steering wheel into the direction of the victim and moved forward, causing the (front) of his vehicle to collide into the rear of the victim's bicycle wheel," the facts state.
"The collision caused the victim to fall from his bicycle onto the ground."
The victim was taken to hospital and found to have sustained injuries to his ribs and left elbow.
Police said Bosnich co-operated with them throughout the investigation.
The case returns to court on 9 June.
Bosnich played for Aston Villa, Manchester United and Chelsea in the English Premier League in the 1990s and early 2000s, before becoming a television presenter.
Outside court Bosnich told waiting media: "It's very, very rare that I've got nothing to say but unfortunately today I haven't. Would you believe that?"