The designs show how the “painted steel” structure would cross Dalry Road, running next to an existing road link.
According to estimates, around £1 million will be required to deliver the 28.5-metre bridge and approach ramps.
The proposal is among a number of planned changes which could cost up to £6m and are aimed at creating an integrated pedestrian and cycle way between Roseburn and the Union Canal.
These include a new crossing over the Mid Calder railway line and construction of a toucan bridge at the Western Approach Road.
Cycling campaigners have welcomed progress on delivery of the Dalry Road scheme.
Ian Maxwell, a member of the Spokes campaign group, said: “This bridge is going to be quite an important link. While any bridge is expensive, we feel that having that link across the road is part of a wider scheme and we would be in favour of it.
“I think it could be designed in a way that will not clash badly with the existing surroundings.
“The current bridge is not a spectacular structure itself.” He added that Spokes members were generally comfortable with the bridge design.
“I do not think there’s any particular problem with the appearance of it,” he added.
“Overall, we are positive about it. It’s one of the things that will make a massive difference to provision for cyclists and pedestrians in Edinburgh.
“It will fill an important gap in the cycling network.”
Residents’ leaders also welcomed the proposals.
Rona Brown, who lives in Dalry and has served as secretary at Gorgie and Dalry Community Council, said she was not aware of any significant concern over the dimensions or look of the bridge.
“We welcome anything that encourages people to get on their bikes and use them, and creates nice routes for people to walk along,” she added.
City bosses said they were currently bidding for funding to deliver the scheme, with a finalised plan incorporating public feedback due to be put before councillors later this year.
Councillor Lesley Hinds, transport leader, said: “The project to create a new shared pedestrian and cycle path between Roseburn and the Union Canal would deliver a new traffic-free link in Edinburgh’s QuietRoutes network.
“This network aims to open up cycling as a travel option to the many people who are put off by heavy traffic, as well as to improve facilities for existing cyclists and for pedestrians.”
She added: “The proposed new cycleway and bridge crossing over Dalry Road would also open up access for local people to green spaces currently isolated on the top of old railway embankments and improve Dalry Community Park.”