Tony, I think with a double-bridge battlefield (where you're on the offensive), you've at least gotta give it a go. You're almost obliged to, for the sake of your main army who are waiting for something (ANYTHING) to happen to allow them to assault. I mean, the enemy's forces are split too...

I find that you either need fast cavalry to try and squeeze through over the bridge before the enemy plugs the gap, or really REALLY heavy cavalry (like Lancers or V2 Armenians) to punch through the enemy, and then run for your life and try to create some space between you and the enemy.

Once you've got some near-full-strength cavalry over the bridge, things become a bit easier. They can harass the enemy's second force and make things generally difficult. You might then be able to push some infantry over to make a mini-battleline and build from there.

It beats the meat-grinder approach on the main bridge any day.