Had a look at the streetview images. 2 lanes going one direction and 3 in the other. You could take the lane if needed while crossing the bridge. The shoulder is moderate and you have a wide enough sidewalk, but getting to that isn't a clear shot, and that is the dangerous part, IMO. Looks like in at least one spot there is no rideable shoulder for a few yards.

I would wait for a gap in traffic on the approach to the bridge, then do a "hold & release" as you cross. You probably will get some angry drivers honking at you when you slow them down by a few seconds.