Bike lanes on bridges make good sense: no intersections and speeding traffic. Also, it is crucial that cyclist can ride over bridges, since there usually are no alternative routes for bridges within reasonable distance.
I don't think a bike lane is too much to ask for. A 15-mph speed limit idea is a joke: it will never happen, and if it happens, it will not work. If there are few cyclists who use the lane, drivers will speed anyway, making it no different from regular lane. If there are many cyclists... then a dedicated bike lane is justified anyhow.
Do I understand correctly that the bridge connects the downtown core and a more suburban part of town? If a bike-friendly route into downtown (and bike-friendly streets downtown) existed, perhaps a lot more people would ride and congestion would actually lessen. At any rate, what's so great about encouraging people to drive downtown? Maybe increasing congestion (while providing safe alternatives) is a good thing.