The deal would see Dublin Bus staff receive pay rises totalling 11.25% over three years.
This is more than the increase of 8.25%, as recommended by the Labour Court.
Drivers have been seeking a 15% pay rise over three years.
The latest deal would not be linked to additional productivity.
Strikes had been scheduled for 11 more days in October, including this Saturday, when Dublin face Mayo in the All-Ireland senior gaelic football final replay.
Under the proposal, staff will be expected to cooperate with the introduction of drug and alcohol testing at work.
Irish broadcaster RTÃ‰ reports that cooperation will also be expected on measures to reduce absenteeism.
The proposal also included items relating to scheduling, pensions, and other policies.
The ballot of Dublin Bus staff is expected to take about ten days.
Hundreds of thousands of people have already been disrupted by a series of strikes by bus drivers in September.
Bus strikes in Dublin have been suspended pending a ballot of staff, after talks between management and unions at the Workplace Relations Commission.