If the bridges are already a bottleneck to get into the city, I think it's a bad idea, just like I think the moronic empty hov lanes we have are a bad idea.
An intelligent solution would be making the right lane bike friendly. Mark it as a bike/car lane with a strictly enforced 15 mph speed limit. Make it know that it is a bike/car lane, as opposed to a car/bike lane. Aggressively prosecute cagers who speed in it or harass bikes.
Making it a 100% bike lane would make sense if there was heavy enough bike traffic, but, if the cagers parked in the other lanes see a cyclist whiz by every 5 minutes, they'd be pissed, as well they should be.