That follows substantial below-ground problems that have pushed completion of the project back to May next year.
The latest stage of the project will also bring changes next month to access from South Rd to Riselaw Rd, and the closure of an intersection at Short St.
The bridge is part of stage two of the Caversham Valley Safety Improvement Project, and will connect Riselaw and Mornington Rds over the highway.
The stage had an initial budget of $23 million, but geotechnical problems, including the discovery of a fault line and underground hole the size of a double garage earlier this year, would make a difference.
NZTA Caversham Highway Improvements Project manager Simon Underwood said he would ''rather not say'' what the cost increase might be.
Stage one of the project widened the highway between Andersons Bay Rd and Barnes Dr to a consistent four lanes.
The second stage is widening and realigning the highway from Barnes Dr to Lookout Point, and includes the new bridge.
A computer-generated image of the bridge - which the agency says will be subject to detail changes as it develops - shows embankments up to 7m high that will be built on either side.
Downer project manager Tony Clough said Dunedin City Council building consent for the bridge was expected by September.
Foundation work should then begin. Seven concrete piles were to be put in place.
The piling work was expected to be finished by Christmas.
Construction of the embankments would take place around the same period.
Mr Clough said the work would involve between 10 and 15 workers at different times, and the bridge - and stage two of the project - should be completed in May.
Other work being done included moving city-bound traffic lanes on to a new area of road that had been constructed on the Mornington side of the highway.
That was expected from mid-to-late August.
The speed limit would be increased to 60kmh on the downhill section.
From early August, there would be two significant changes to traffic movement near Lookout Point, Mr Underwood said.
Short St, which runs from Kaikorai Valley Rd to the highway, would be closed permanently at the highway intersection.
From August 1, South Rd would no longer connect directly to Riselaw Rd.
Instead, drivers from South Rd wanting access would need to go via the highway and an off-ramp back on to Riselaw Rd.
That change would be permanent.
Mr Underwood said while the road and bridge work was being done, the city council was continuing upgrade work on water and drainage infrastructure, some of which was a century old.
