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.

Workshops are being held at the the city's Royal Cornhill Hospital using specially modified goggles, gloves and other equipment to simulate symptoms.
It is aimed at carers and those who have friends or relatives affected by the condition.
Staff say the equipment frequently leaves people with a completely new understanding of the disease.
Participants are asked to fulfil basic tasks such as getting into bed, writing their name or buttoning up clothing.
Julia Wells, an older adults mental health nurse consultant with NHS Grampian, said: "With the number of people living with the disease expected to double over the next 10 years, it's vital that we do everything we can to raise awareness of dementia.
"Dementia Awareness Week in general and workshops offer a great platform to do just that.
"It also helps to reduce some of the stigma that still exists around the disease."

Photos shared by local media show copies of the Islamic holy book in three toilet bowls.
Campus police say the case is "strange" and "very unusual" due to the religious and ethnic diversity at the school.
Police are trying to identify one of six people seen entering the toilet on the evening of the incident, 28 March.
Investigators have been reviewing security footage to find a suspect.
X-Men artist fired over Koran verse
A reflection room where multi-faith prayer books are kept on the building's ground floor was not touched, according to investigators.
Police Chief Larry Zacharias told the Dallas Morning News: "No one knows who owns the books, so that makes it difficult."
Mohammad Syed, president of the college's Muslim Student Association, told local media the case was "definitely saddening and a little disturbing as well".
"While there is a little voice of hate, there is an overwhelming voice of love and support and we definitely appreciate that," he said.
Why was Koran ripped up at school meeting?
He added that the university is "a very welcoming environment".
The Korans were discovered by members of the student government after an evening meeting.
"I was appalled," said Jonathan Schuler, who found the sacred texts in the toilets.
"It made a lot of the hate I had been hearing and seeing on national news real, and very present."
The student senators have released a statement calling it an isolated incident that does not represent the university community.
'I escaped death by reciting from the Koran'

HIE along with other public bodies are to be run by a single board under Scottish government plans.
The government has said services already provided in the Highlands and Islands would be protected.
Scottish Lib Dem leader Willie Rennie unveiled the petition on a visit to Inverness.
He and his party argue that decisions on HIE should be taken by a board based in the Highlands and Islands.
In October, the Scottish government set out plans to reform Scotland's enterprise and skills agencies in a report on Phase 1 of its Enterprise and Skills Review.
It has proposed setting up a new single Scotland-wide statutory board to co-ordinate the activities of HIE, Scottish Enterprise and other public bodies.
HIE began as Highlands and Islands Development Board more than 50 years ago. It supports businesses and initiatives in the Highlands, Western Isles, Northern Isles, Moray and Argyll.
Bus strikes in Dublin have been suspended pending a ballot of staff, after talks between management and unions at the Workplace Relations Commission.
[NEXT_CONCEPT]
A kit which allows people to experience what it is like to have dementia has been introduced in Aberdeen.
[NEXT_CONCEPT]
Police are investigating after copies of the Koran were found in toilets in the student union building of the University of Texas at Dallas.
[NEXT_CONCEPT]
The Scottish Lib Dems have started a petition supporting calls for Highlands and Islands Enterprise (HIE) to keep its board.