The AI seems a bit challenged when it comes to bridge battles. I was defending against the Golden Horde and only had enough troops to defend one bridge but I was on a two bridge map.
I put all my men in front of one bridge and the silly AI never once tried to flank me by using the second bridge.
I still lost the battle because I didn't have enough men, but I killed hundreds of the GH and even routed them a couple of times, only to have their reinforcements drive me back across the bridge.