On bike, I have crossed bridge to Surfside from mainland, and have crossed San Luis Pass bridge, on a ride from Galveston, and on another trip from Surfside.
Things went pretty well. On San Luis, traffic gave me space. There is a good shoulder on Surfside bridge.
Debris collects along the sides of these bridges - for the most part, it cannot just get blown away like on a regular road. So, the edges can be trashy. If you ride a bridge with these conditions, you need to be wary if you feel tempted to go fast on the descent.
Bridges can be very windy. And, gusty. So, you need to be prepared to get hit hard at any moment by wind. I have ridden across Lake Ray Hubbard, metroplex, on 66, and been hit hard by gusts.