Sydney commuters should expect chaotic travel conditions on Thursday afternoon as bus drivers stay on strike despite two Industrial Relations Commission orders to return to work.

About 1,200 drivers have walked off the job in protest over the NSW government’s plan to privatise services in the city’s inner west and south.

The stoppage, which began at midnight, affects four depots in Leichhardt, Burwood, Kingsgrove and Tempe, and left Thursday morning commuters stranded at bus stops during peak hour and school times.

Much of the same is expected for the afternoon, with Transport NSW’s CBD coordinator general, Margaret Prendergast, advising commuters to allow “plenty of travel time,” despite a limited private bus service running along Parramatta Road from Five Dock to Burwood into Railway Square.

“We’re really hoping bus drivers do turn up to work this afternoon and we will prioritise those buses to really service the school service run so that we can get the kids home this afternoon,” she told reporters in Sydney.

The Industrial Relations Commission late on Wednesday ordered the drivers not to strike, claiming it was “illegal” and sent another order on Thursday morning, advising drivers to return to work, otherwise they would face “legal consequences”.

But Rail, Tram and Bus Union (RTBU) NSW divisional president David Woollams said the drivers remain committed to the stoppage.

“Physically, it would be too big of a job for us to try and physically ring everyone to get them to come back to work,” he said.

“Even if that was to be the case, the members of these four depots are adamant they are not coming back to work today.”

At a meeting of its members, the RTBU divisional secretary, Chris Preston, apologised for any inconvenience caused by the strike.

“This action is on [NSW transport minister Andrew] Constance’s head.”

Responding to the commission’s orders, Preston told members to return to work at the meeting but those members present shouted “No”.

“I’ve asked you to go back to work. I’ve complied with the order,” Preston said.

Constance told reporters the members have shown “contempt for a court ruling” and should “go straight back to work”.

“If we have to go to the supreme court this afternoon, that we will do,” he said.

The Greens have come out in support of the strike, with Mehreen Faruqi saying in a statement the privatisation of bus services “will be a disaster for workers, drivers and the public”.