I usually prepare for possible bridge battles by bringing in some good old mercenary meat. Usually bit better units are good since AI will start shooting arrows into big melee which, hopefully, starts at the bridge and when you start throwing in arrows as well there will be lots of corpses there. Once enemy has exhausted itself go in with heavy troops and cross the bridge fast.

On a little different topic, AI desire to acquire higher ground for defence is sometimes really stupid. Once it decided that best spot to defend is behind my army. I nearly panicked when I noticed that they were coming in while I was still preparing for my attack until I noticed that they were trying to pass my army without a battle.

Needless to say I took the opportunity and assaulted their flank while they marched.