Drivers and management at Bus Éireann will attend talks at the Workplace Relations Commission (WRC) today.
Unions had planned an all-out strike from this morning in a row over cost savings at the company.
The strike has been postponed to allow negotiations take place.
The bus company says it needs to make savings of €30m a year to stay afloat.
Dermot O'Leary from the NBRU says he isn't overly optimistic.
"We did explain to the company the other day that the €30m savings that came out in recent weeks was not a runner for us," he said.
"Our job I suppose is to go in and discuss the Expressway crisis and if that's the approach by the company then hopefully we will try and make some progress but, again, I don't want to be giving false hope to people."