Typically not an isolated phobia but one component of a constellation of anxiety disorders, and often causes suffers to take elaborate routes to avoid meeting a bridge. Can also encompass fear of passing under bridges, or panicking while on a bridge. Coined, as you might expect, from Greek roots (there are very few Latin-derived phobias) gephyra, bridge + phobos, fear. For a usage example, I steal from Wiktionary's entry, because it is true:
Venice is a place to avoid if you suffer from gephyrophobia.