Well, I assume your question is directed to the situation where you are the attacker, if you are the defender, the AI will most likely come to you.
When you attack at bridge maps (never an easy job), you should make sure to check on what and how many troops the AI has stationed in the province (always a good idea to wait a couple of turns, the AI might deploy some troops to other locations so making the assault easier for you), and then choose your own force accordingly. I've found that bridge battles often require specially designed armies, contrary to other occasions where you just throw all ragtag units you have into the fight, knowing you will probably win in open terrain..
You should definitely bring at least 4 missile units, (archers, but preferably arbalesters due to their superior range), your best spear and shock units (upgrades and all..) and perhaps a light cavalry unit.
March towards the bridge and see if you can hit the enemy's units without having to cross the river, if you can, fire away. Then you should set up one unit of spearman flanked by a shock unit on both sides immediately in front of the bridge. Now, you can send a fast unit (your light cavalry, preferrably) to the other side and close in on the enemy.
The AI should dispatch a few units to engage you, but don't join battle, instead retreat slowly towards the bridge. Usually they should follow you and that's where you can hit them with missiles (if they set up out of your range initially).
If they retreat, just move your scout unit ahead again.
If you are good, you can get them to follow you across the bridge, then you can start attacking them with your spearmen or shock unit. Usually, that's the point where the AI will mobilise all of its remaining forces and head towards the bridge and that's when you've achieved your primary goal of turning from attacker into a defender.
It should be easy to hold the bridge and decimating the enemy forces until they start routing. When they do, you can cross the bridge and set up on the other side, in case they rally or reinforcements do arrive.

Sometimes, this strategy doesn't work, and you have to resort to brute force to gain a foothold on the other side of the river. In that case, be sure you bring tougher (and more&#33 troops as well as a better general (the general's number of command stars has a huge effect on his troops).

If you can't muster all of this, then don't fight that bridge battle at all. You must have a clear advantage if you want to attack at a bridge map.