There are lots of bridges of this nature in my area, one I cross regularly is about 1/4 of a mile long, and another is long enough that it takes a long time to cross, has a couple curves, expansion joints that can eat a 23mm tire, and drainage grates that will swallow a 35mm tire if hit wrong. None of these bridges has a shoulder wider than that in the picture. Oh, and no signs warning motorists of a cyclist on the bridge. My head might explode with wonder and joy if I ever saw that here.
I usually ride in the right hand tire track at the beginning, but am often eventually all the way over to the right by the end of the bridge. This is because for some reason many motorists will insist on passing regardless of where in the lane you are, and usually with similar disregard for oncoming traffic. There is a mindset here that seems to say that if you are on a bike you are to be passed. When a car does wait behind for a clear shot at going around, then often the drivers behind will simmer and stew, then go around in a line following the lead car, even when oncoming cars get to close. When I see an scissor coming up from none of the drivers wanting to give ground, that's when I tend to give up the middle of the lane and get over more to the right. I gave up on any hope when a state trooper once was part of the passing line, middle of about five cars. Arkansas. All I can figure is that cyclist are so rare no one knows how to deal with us. Of course, when traffic is light, I will move over some to the right for an upcoming vehicle as a invite to go around.