Are you looking for in-game suggestions to collapse the bridge, or some suggestions for running an encounter on a collapsing bridge? Or both?
To collapse the bridge, fire spell charge as HoboGod suggests could set a wooden bridge on fire. In that case you're dealing with a fiery battle field, which could be really exciting. If the bridge is stone, then maybe a well-placed
rock to mud at the base of the supports; that could give a X% per round that a portion of the bridge will topple and start the whole thing collapsing.
For collapsing parts-- whether because of fire or weakened stone-- you could run it like an "expanding pit trap" grows and slowly "eats away" at the bridge. In round 1, a 10x10 hole opens up. In round two, the ground within 10ft of the original hole opens up (so now it's 20x20). Round 3 it expands to 30x30, and so on. Each round, anyone on the collapsing part makes a reflex save to leap to a stable part of the bridge, or else ends up in the river below.
If you have a little more info, I'm sure others will have some ideas. In any event, sounds like a fun encounter!