Admittedly I haven't crossed the bridge in the last few years, but used to ride across pretty regularly and never had a problem—just remember to claim the lane across the vertical lift section. And cross the rail lines at a right angle, naturally...
There are four phases of bicycle commuting; first there's fear, then rage, then self-righteousness and finally, fun. -Yehuda Moon
I reckon Danny's attempt was a bit lame -- you've got to do it above the water to look really cool. Hence the Bridgewater Bridge. Oh yeah, and on a roadie, none of those soft trials bikes with suspension for me.
This used to be my daily commute in the sun and in the ice/wind. I found the causeway to be fine, just stay upright in the wind. The real trick, I had to learn more than once, is that wet train lines at 45 degrees to the road are not cool. I tackled them in the end by looking over my shoulder and if no cars we behind me I would vere across the lane to put the train lines at 90 degrees under the wheels. Also not cool if you forget to look behind.