SAN FRANCISCO — Long the holy grail for cycling advocates in the Bay Area — a bike and pedestrian path spanning the entire length of the Bay Bridge, offering unparalleled views of San Francisco and a carbon-free alternative to soul-sucking traffic — has, for decades, remained tantalizingly out of reach.

It’s seven miles from Oakland to San Francisco, but with the east span’s bike path ending halfway at Yerba Buena Island, the remaining three miles to San Francisco on a bike might as well be a trip to Mars. Early cost estimates for the path were astronomical and technical challenges loomed large.

The project got a little bit more grounded, though, with the release of a study that will be presented publicly for the first time on Monday. The study shows it is technically possible to build — but it won’t be cheap, and it won’t be easy.

Cost estimates for the roughly three-mile path range from $341 million to nearly $429 million, figures that could rise as the design gets closer to completion. There are numerous other challenges, including how to attach the new path to an 82-year-old bridge and how to manage construction in a corridor traversed by more than 266,000 motorists every day — not to mention how to pay for it.

But, with the potential to support upwards of 10,000 bicyclists and walkers daily, the benefits, cycling advocates say, “would mean everything.” With the advent of electric-assist bicycles, the idea of biking the entire seven miles from San Francisco to Oakland is no longer just for the most devoted riders, said Brian Wiedenmeier, the executive director of the San Francisco Bicycle Coalition.

The study estimates it would take an hour on an electric bike for commuters to reach San Francisco from as far as Pinole to the north, Lafayette to the east, and Hayward to the south. On the San Francisco side, it would take the same amount of time for riders in Daly City and South San Francisco to reach the East Bay.

“It’s not just for the hardcore folks in Lycra who could make this part of their daily commute,” Wiedenmeier said. “And, that view will take your breath away.”

This study is not the first time the region’s transportation planners have looked at the potential of building a path along the Bay Bridge’s western span, but Monday’s presentation will be the closest they’ve come to understanding the full magnitude of construction and its associated costs, said Karin Betts, a spokesperson for the Metropolitan Transportation Commission (MTC), the region’s transportation planning agency.

Two studies in 2001 and 2011 looked at options for a path, including where it might land in San Francisco, how it would connect to Yerba Buena Island, and how the path would attach to the bridge. Renewed interest for the west span path picked up in 2013, when the east span, with a bicycle and pedestrian path from Oakland on the south side of the bridge, first opened to the public. In 2016, the path reached Yerba Buena Island, where a suite of improvements are planned to accommodate a protected bikeway to Treasure Island.

The most recent study takes it a step further, Betts said, by selecting a preferred alternative and completing up to 25 percent of the engineering designs in some places along the span. Under this plan, the path would meet the eastern span on the south side of Yerba Buena Island before wrapping around to the island’s north side. From there, cyclists and walkers could turn to Treasure Island or head west to San Francisco.

The path would then follow the bridge to the Fremont Street off-ramp and finally touch down on Essex Street, where cyclists could connect to San Francisco’s network of bike lanes.

Along the way, engineers would need to erect steel cantilevers on the north side of the bridge that would bolt into the bridge’s steel frame, said Peter Lee, the MTC’s project manager for the west span bike path. Because of the steel’s age, crews can’t weld onto it, he said. There’s layers of lead paint that need to be carefully managed and an increasingly shorter nightly construction window as worsening traffic congestion continues to lengthen the definition of “peak commute hours.”

But, one of the biggest challenges is the extra weight, which could lower the height of the suspension bridge by as much as two feet and make it hard for large cargo ships to pass safely underneath.

“Maritime traffic was here before we had the bridge,” Lee said. “Even in the last couple of years, we’ve had ships go underneath that have only cleared it by a few inches.”

The weight of the path can be offset by lightening the load in other places, he said, such as resurfacing the roadway with a new, lighter-weight asphalt, which would be part of the bridge’s regular maintenance. This new study allows planners to take the potential path into account when making those upgrades, Betts said.

“These feasibility studies are a starting point,” she said. “They aren’t intended to be an ending point.”

Watch the presentation live:

Registration for the event, which will be held at MTC’s offices in San Francisco, is now closed. Viewers can watch the presentation live online at Facebook.com/MTCBATA. To be notified when the presentation begins, respond to the MTC’s event on Facebook at: https://bit.ly/2ERGTWD.