Bus Éireann unions say a recommendation from the Labour Court today could see pickets lifted.
Both parties in the dispute are due before the court within the hour, on what is now the 20th day of strike action.
The NBRU says that any recommendation is likely to be complex and will take time for their members to consider.
General Secretary Dermot O'Leary said: “It should be understood that the reason for the dispute was because people had conditions forced on them without agreement.
“Now, if that changes over the next day or two, along with the recommendation, you would imagine … there would be pressure on, and an obligation, indeed, on the trade unions to lift the pickets.
“And we will not be found wanting in that regard.”
A Labour Court hearing into the Bus Éireann dispute will resume this morning.
Strike action at the company has now entered its 20th day, with thousands of commuters still facing travel disruption.
Unions say they want the court to look at the issues of rostering changes and consolidated pay, saying they constitute major changes which require some type of reasonable salary.
SIPTU's Willie Noone says their stance is clear.
"We have said, quite openly, that once we went on strike, we would not be leaving the picket until two things happened," he said.
"One was that we had proposals where members could actually decide, once and for all, whether they [the proposals] were good enough to go back and continue working in Bus Éireann, and number two that they were not going to go back in under the threat of cuts - that whatever cuts were being proposed would have to be taken off."