Charity Bristol Mediation has been given Â£10,000 of public money to "bring road users together".
But doubts about the plan have united some. Cyclist Hugh Marshall called it a "cosmetic exercise" and the Alliance of British Drivers said "it's a joke".
The council said it looked forward to "seeing positive results".
Bristol Mediation, which helps neighbourhoods to resolve conflicts and disputes, is running the Road Sharing Restorative Approach scheme.
It said the city was well known for its clogged streets as cars, bikes, buses, taxis and lorries competed for space which "can lead to road rage and conflict".
Some road users who spoke to BBC Bristol did not think the project was a solution to the issue.
Mr Marshall, who has been cycling for 40 years, said there had been an "explosion in cycling" in the past five years and suggested an adult cycling test.
"Quite a good percentage of these new cyclists are either contemptuous of the Highway Code, or completely ignorant of the Highway Code," he said.
Bob Bull, from the Alliance of British Drivers, said: "The problem is that cyclists can do what they like, where they like, when they like and there's no repercussions. That clearly isn't the case for motorists.
"These are the circumstances that breed people's feelings, so you end up with the situation where motorists are seen as anti-cyclist. It's a complete waste of money."
The project, which will also produce a short film, is one of several community safety projects to be awarded funding from the office of Police and Crime Commissioner Sue Mountstevens.
The council, part of the Safer Bristol Partnership which distributes the money, said it was "always supportive of any project that encourages positive relationships between all different road users".
Cyclists and drivers are being asked to find ways to share Bristol's "congested streets" without resorting to road rage.