Four days of talks have been scheduled after discussions on Monday. Union officials said there was "scope to make progress".
If the sides fail to reach a deal, a strike on Saturday is set to go ahead.
Hundreds of thousands of people have already been disrupted by six days of strikes by bus drivers in September.
Strikes are scheduled for 11 more days between now and the end of October.
Drivers are seeking a 15% pay rise over the next three years.
Dublin Bus has said it cannot exceed an increase of 8.25%, as recommended by the Labour Court.
In a statement, the firm said it would continue to engage "in an effort to find a resolution to this current dispute".
Owen Reidy, from trade union Siptu, said there was a "considerable way to go" in the talks but that the decision to suspend strikes was taken because unions felt there was "scope to make progress".
Irish Transport Minister Shane Ross said the decision would bring relief to the "travelling public, businesses and all those who have been adversely affected by the recent strikes".
Bus strikes in Dublin scheduled for Tuesday and Wednesday have been suspended to allow for negotiations aimed at resolving the pay dispute.