ABC newsreader Jeremy Fernandez says a Sydney bus driver told him he should have moved seats when a woman was verbally abusing him during a 15-minute racist rant yesterday morning.

Fernandez took to Twitter to express his dismay at the attack, which started when he asked the woman to keep an eye on her daughter, who he says was clipping his two-year-old daughter on the head.

"And she just went on this rant and told me, 'How dare you? What are you doing looking at my daughter? Have you been touching her, have you? Do you fancy five-year-olds?'," he said.

"I just thought, 'Oh my God, what have I done? I've picked a fight with someone who's mentally unstable', and I thought I should move. This is not worth ruining my Friday morning for."

He says that as he was contemplating moving seats, she told him to "go back to his country" and called him a "black c***".

Fernandez says he decided not to move, drawing on the example of US civil rights activist Rosa Parks.

"It was really nice to draw on a strong woman and think what would she have done," he said.

"She stayed in her seat. I'm going to stay in my seat.

"The bus driver stopped at one point and said, 'You, get out of your seat and move,' and I said, 'I'm not moving anywhere, I haven't done anything and I'm staying on this bus because I have a right to be here, and she just called me a black c-word so I'm staying put'."

After the woman got off the bus he approached the driver.

"I said 'Look, you have carriage for everyone on the bus. I've just been racially abused for 15 minutes on the back of this bus and you did absolutely nothing'," he said.

"And he said, 'It was your fault - you didn't move'.

"I said, 'I was going to move but when it became a racial issue I refused to move'."

Fernandez described the incident as "my own Rosa Parks moment" and said he wished his two-year-old girl had not been there.

"I thought, 'Oh my God, this is the introduction of a lifetime of her understanding what hate is about'."

Such racism on public transport is not unheard of.

Last year a group of backpackers was dealt a tirade of abuse from passengers after singing in French on a bus in Melbourne.

President of the Human Rights Commission and acting Race Discrimination Commissioner, Professor Gillian Triggs, says she is concerned by what appears to be an increasing number of racist remarks being made in public settings.

The bus driver in Fernandez's case blamed the victim for not moving, but Professor Triggs suggests there is a positive role for onlookers.

"Where it's not going to put the person in harm's way - we certainly wouldn't recommend that - but nonetheless, if a person can reasonably say, 'Hey, that's unacceptable. You've gone too far', then we think that this could help to support the person who's being abused and perhaps even help to defuse the situation."

New South Wales Transport Minister Gladys Berejiklian says she wants to hear from Fernandez.

"I've only just learned of it and am absolutely horrified to hear what he and his daughter went through. I can only imagine on a personal level what they would have felt like and I am really horrified to hear it happened here in New South Wales," she said.

She says the bus driver can contact security if they have a concern about passenger behaviour or use their own discretion to kick someone off the bus.

Fernandez says he is pleased he has the profile to be able to bring attention to the issue. He says there are many out there who do not.