Bridges can be scary places. I know off one incident were people have been blown off perfectly stable bridges, while they were cycling on them. (well only one case, a road racer in the 1920ies, riding accross the newly finished motorway Heidelberg to Manheim to practice. He was to fast down a hill and a gust just grabed him and blew him down.
Séguin's Tain-Tournon Bridge, a double suspension span over the Rhône, completed in 1825. Its 1847 replacement still stands, probably the oldest wire-cable suspension bridge in the world, with its carefully replicated wooden stiffening truss and deck. Several of Séguin's first-generation wire-cable suspension bridges, dating from the 1830s, remain over the Rhône at Andance and Fourques, but the decks have been replaced with steel.
Same source, tough I don't know whether vehicles still use this one:
The oldest suspension bridge extant today is the Union Bridge over the River Tweed at Berwick (UK), a chain-link bridge designed and erected by Captain Samuel Brown in 1820, with a span of 449ft (137m).