Seiges I hate because all the enemy just retreat away from your walls and force you to fight on level terms, unless you have lots of archers it can get drawn out and boring.
But seriously, bridge battles are very easy and fun because the AI always tries top rush the bridge. All you need to do is hold your side of the bridge and you win. Just have your spearmen and swordsmen guarding your shore in sheild wall and the enemy will always cross and try to attack you, but can never break through because they get bottlenecked and mixed up. Once they hit your lines break shield wall and you can prevent them getting a foothold
Have archers on the flanking shores to take out enemy archers and soften up them men stuck on the bridge, and have your calvary ford the river and attack from the rear, the enemy panic as they are trapped and you can destroy them. If you have catapults it's a bonus as you can do more damage as the enemy cross and retreat due to them being so bunched up.