The hood canal bridge in Washington is a retractable (and floating) bridge, so that would be the fourth example.
I only know of three genuine retractile bridges in the United States. This bridge, the Borden Avenue Bridge also in New York City, and Boston's Summer Street Bridge. A lot of sources claim there are four examples, but I don't know where the fourth example is. One source I found made me suggest that somebody has mistaken Chicago's Rall bascule bridge as a retractile bridge. If anybody knows of a genuine fourth retractile bridge in the United States I would be curious to know where it is.
Actually, this is a retractile bridge, a dying breed.