Services will run as normal tonight, Tuesday and Wednesday
The NBRU say planned Dublin Bus strikes for tomorrow and Wednesday have been called off.
The union has agreed to suspend 48 hour stoppage in order to engage in "intensive and comprehensive discussions" on a settlement of the dispute.
Services were due to stop at 9.00pm Monday, but they will now run as normal.
Unions and management met at the Workplace Relations Comission (WRC) for exploratory talks.
Dublin Bus management say they will continue to engage with all parties at the WRC over the coming days "in an effort to find a resolution to this current dispute".
"All Dublin Bus services will now operate as normal tonight and Tuesday 27th and Wednesday 28th September", it says.
Transport Minister Shane Ross has welcomed the decision.
In a statement from the Department of Transport, it says Minister Ross is "cognisant of the relief this will bring to the travelling public, businesses and all those who have been adversely affected by the recent strikes.
"He appreciates the role played by the WRC in facilitating these negotiations and hopes that all sides are given the appropriate space to arrive at a solution that is fair and achievable," it adds.
NBRU General Secretary Dermot O'Leary said: "In agreeing to suspend our member’s industrial action we are placing our trust in the WRC and its assessment, following its separate exploratory discussions with Dublin Bus, that significant progress can be achieved over the next number of days in order to find a resolution to this dispute.
"The onus is now very much on Dublin Bus to come to the negotiating table and step up to the plate to go significantly beyond what has already been rejected by all of the Staff and work with the Trade Unions towards achieving a satisfactory resolution of this dispute, falling short is simply not an option for commuters and staff alike".
And SIPTU adds: "While industrial action is scheduled for Saturday next (1st October), SIPTU and other union representatives are hopeful that progress can be made in discussions which can facilitate the cancellation of further planned stoppages at Dublin Bus."
However further work stoppages are planned for Saturday this week - as well as 10 more days next month.
It comes as businesses in Dublin city say they saw a loss in sales following the bus strike last weekend.
Dublin city's Business Improvement District (BID), DublinTown, say footfall figures were down by 9% on Friday and 16% on Saturday.
Drivers are seeking a 15% pay rise over the next three years - as well as a payment in lieu of an agreed 6% increase that was deferred in 2009.