彼は橋を渡った。

I would say「彼(かれ)は 橋(はし)を 渡(わた)った」as well. In Japanese you always 渡(わた)る a bridge, no matter you walk or drive. If some says they 橋(はし)を渡(わた)った、you can tell that they went over the bridge, but you can't tell if they walked, drove or what. You can make it clear whether he WALKED or DROVE across the bridge by adding a verb. > He walked across the bridge.　彼(かれ)は 歩(ある)いて 橋(はし)を 渡(わた)った。 > He drove across the bridge.　彼(かれ)は 車(くるま)で 橋(はし)を 渡(わた)った。