I've noticed the AI very rarely makes use of fords and alternate paths in a bridge battle. It's also sluggish to defend them when, on the flip side, you use them against it. The general AI defense on a bridge seems to be to skirmish with ranged units while you push toward the bridge. Once you make your move, to either continue to lay down fire or withdraw to a main line - and then its business as usual.

When the AI defends it's a very 'passive' defender, giving up the crossings with little fuss in my experience and only really pushing you once you've redrawn your lines on the other side of the river.

When it attacks it's nearly suicidal, throwing everything at you at once. While the field AI isn't perfect it's usually much more reserved than it is in a bridge attack.