A woman whose racist rant on a crowded Sydney train in July shocked the city has escaped without a conviction after telling the court she was "absolutely appalled" at her behaviour.

Karen Bailey pleaded guilty at the Downing Centre Local Court to one charge of offensive behaviour on Thursday morning.

Remorseful: Footage posted on Youtube shows Karen Bailey during her racist rant on a train.

She was arrested at Wyong train station early this month after a racist and expletive-laden tirade at a commuter of Asian descent.

The rant was captured by another passenger and the footage scorched across the internet.