Miami-Dade commissioners agreed Wednesday to waive the county’s usual competitive bidding process — and to hike tolls on the Rickenbacker Causeway — to speed up and fund repairs on the bridge to Key Biscayne.

The county will expedite bidding, giving firms about two weeks instead of the usual six or so, to submit offers to rebuild the beams and roadway of the Bear Cut Bridge.

The project’s price tag went up to $31 million from $25 million Wednesday. Of the additional $6 million, $3 million will go toward moving a pipe underneath the bridge.

The other $3 million will pay to widen the eastbound side of the bridge to create a new walled-off bike path in addition to the existing pedestrian sidewalk. The county’s plans already included widening the westbound side — which was partly shut down earlier this month — to include protected pathways for cyclists and pedestrians.

The latest plans aim to shift cyclists to the protected paths from existing on-street traffic lanes designated for bicycle use, though cyclists would not be prohibited from riding on the roadway with cars, Gaspar Miranda, an assistant public works director, told The Miami Herald. The existing on-street bike lanes will be used as the shoulder for auto traffic.

Public works administrators had offered a different plan to cyclists and pedestrians at a Tuesday evening meeting of a Metropolitan Planning Organization advisory board. But that was before the administrators and Miami-Dade Mayor Carlos Gimenez attended a Key Biscayne Village Council meeting later Tuesday night. Based on the comments from Key Biscayne council members and residents, the county decided on the new, protected pathway plan Gimenez presented to county commissioners Wednesday, Miranda said.

Gimenez called the new paths “prudent” for a bridge where some cyclists have been killed after being hit by cars. “On both sides there’ll be separation between pedestrians and bicyclists,” he pledged.

At least one cycling group said Wednesday they oppose any elimination of designated bike lanes on the bridge roadway, a popular biking venue.

Earlier this month, the county partly shut down the westbound lanes of the bridge connecting Virginia Key to Key Biscayne in an emergency move prompted by accelerated corrosion of the exposed steel beams, or girders, that hold up a portion of the roadway. The westbound lanes of the bridge were built in 1944; the eastbound lanes, which the county says are structurally sound, were built in 1983 on concrete-encased beams.

Commissioners, who have been weighing blame in the matter, continued questioning public works department engineers Wednesday over how the corrosion problem became so dire so quickly. Antonio Cotarelo, the interim county engineer, suggested that the tar rubbed on the beams to protect them from saltwater may have hidden the extent of the corrosion.

Even with the sped-up bid process, which could open to bidders as early as this week, the county expects the repairs to take a least a year. Gimenez said he hopes the project will be completed before the 2014 Sony Open tennis tournament at Crandon Park.

However, he added: “I can’t guarantee it will be done by tournament time next year.”

The mayor of Key Biscayne, Frank Caplan, urged commissioners to back the expedited bid process, calling the bridge his village’s “carotid artery.”