First mark your unit(s) and then click on the bridge. Now the selection field "Bridge options" appears. Here you simply click on "Destroy". Once the bridge is destroyed, it will take 15 hours before it is complete again.
Important: Vehicles that are on the bridge while it is falling apart are completely lost.
Tip: Vehicles that are specialized against basic defense are also specialized against bridges. Howitzers and Zuzannas are the easiest way to destroy bridges.