Talks between the company and unions broke down earlier this week.
The National Bus and Rail Union (NBRU) has expressed "outright disgust" at Bus Éireann, accusing them of attempting to "provoke a significant cohort" of its members into a reaction.
Talks between the company and unions - including SIPTU and the NBRU - at the Workplace Relations Commission (WRC) broke down earlier this week.
The board of Bus Éireann said it sought written clarification from unions regarding their position.
In a statement, the board said: "Subject to this clarification, there may be an opportunity to re-engage in time-limited talks.
"The Board will re-convene again to approve the implementation of cost saving measures, which must be taken to avoid the risk of insolvency," it adds.
However, in a statement released today, General Secretary Dermot O'Leary said the NBRU "will not take lectures from anyone in Bus Éireann’s managerial structure".
"To call the events of those seven days negotiations is perhaps a reflection of those who are now behind the wheel at Bus Éireann and the inability to differentiate between prevarication, obfuscation, stonewalling and actual negotiating," he said.
"The NBRU has always relied on the industrial relations third parties of the State to provide an honest assessment of any process they have facilitated. Unlike others, we would not seek to use or abuse these institutions for narrow self interests."
Mr O'Leary said the union is committed to engaging in discussions, but say they will not "be dragged into a series of negotiations through the exchanging of correspondence".
"The time being wasted here would be better served around the negotiating table at the WRC, where all issues, inclusive of the necessity for real and tangible commitments around the Burden sharing expected from the significant number of managers at Bus Éireann can be properly coursed," Mr O'Leary concluded.