The call comes as controversy continues to surround the deal struck between the local authority and outdoor advertisers, JC Decaux.
Billboard sites worth an estimated €100m are being handed over by the council in return for 450 bicycles.
The bikes, which will not be available for another year, will be provided free of charge to members of the public for short journeys through the city.
Labour's Sean Kenny, who is chair of the council's transport committee, said he would like to see more transparency surrounding the deal.
"I know there is commercial sensitivity but I sometimes do not buy that line. I would be in favour of the information being made available to the public," Mr Kenny said.
But he said a priority should also be getting the bike scheme up and running.
"It has been a success in Paris and Barcelona. There is a need for it. I would like to see that moving forwards quickly," he said.
Stuart Fogarty, of AFA O'Meara, Ireland's largest advertising agency, has questions about the deal.
"They will be the most expensive bicycles in the world. Those advertising sites are worth at least €100m and we are swapping them for a few hundred bicycles, a few advertising panels and some signage for tourists," he said.
"There are too few bicycles to make any real impact on traffic, so what's in it for Dublin?"
His reservations have been echoed by An Taisce, the Dublin City Business Association, the National Council for the Blind in Ireland, popular architectural website Archiseek and a number of city councillors.
In exchange for 450 bicycles, Decaux has been given 72 lucrative advertising billboards, which have already sprouted up around the city.
Labour's Andrew Montague, who is chair of the council's Cycle Forum, agreed with Mr Kenny that the agreement should be made public.
"The terms of the deal are not public. All we know is that there were five companies that put in a tender. (JC Decaux) was the best tender so it seems like it was a good deal. If it was such a bad deal why would someone else not have had a better deal?" he said.
Comparisons have been made with another city with a similar bicycle scheme.
As part of the Velov scheme in Lyon, JC Decaux has provided 3,000 bikes in exchange for exclusive advertising opportunities in the city centre at 350 sites. Mr Montague said the French city's initiative has had a positive impact on traffic.
"Their scheme started with 2,000 bikes and there are now 3,000, which is testament to its success. It's disappointing that we will begin with just 450," he said.
His Labour colleague Emer Costello said: "We're paying too high a price. We're selling our streets for a few hundred bikes and we have no idea how much JC Decaux is making."
She accused the council of failing to carry out a cost-benefit analysis.
"The project was brought in through a strategic policy committee but it was never voted on by the entire council," said Ms Costello.
"The unsightly signage has been placed disproportionately in the north inner city but its local area committee was never consulted."
The council has said the JC Decaux deal was the best on offer after competitive bidding. It said it will carry out a cost-benefit analysis once the bicycles arrive.