"This sort of behaviour, namely offensive language, is not acceptable," a spokeswoman told Daily Mail Australia on Sunday.
However, Anthony Potts tweeted in the unidentified woman's defence. "Well, she was p***** as they didn't pay for their ticket," he said. "How is that racist?"
Another social media user, Hildander, who campaigns against multiculturalism on Twitter, likened the footage to a left-wing conspiracy to get attention.
"Overplaying it too much. The left are constantly pulling this s*** to stir up trouble," he said.
However, Nine News Adelaide reporter Brevi was disgusted with her behaviour. "This is a disgrace. Just part of a racial attack filmed on an Adelaide bus yesterday," he said. "It goes on for almost two minutes."
Adelaide Metro has vowed to find the woman responsible. "AM will not tolerate abuse of this kind. We'll work with the police and the service provider to identify the person responsible," they tweeted to the Nine reporter.
Another tweeter, Flickus Delcon, blamed US President-elect Donald Trump, who during the election campaign likened Mexicans to rapists and proposed a temporary ban on Muslim migration.
Joshua Michalski tweeted: "She is part of the reason I don't take public transport."
The woman's broad Australian accent caused more offence. "God, she even has the whiny nasally bogan voice," salmonfc tweeted.
Delfac downplayed her behaviour. "Drunk bogan housos are such a serious threat? Give me a break," he said.
A spate of racist attacks have taken place on Australian public transport in recent years.
In February 2013, a female bus passenger in Sydney called ABC television newsreader Jeremy Fernandez a "black c***" in front of his daughter.
In July, a 19-year-old Brisbane man at a bus stop endured being told he should "go back" to his own country after replying that his father was born in New Zealand.
