When I attack a bridge I figure that the units most dangerous to me are the missiles, followed by the spears.

I usually attack with two stacks:
Army 1: Two Pike Units -- One to guard the bridge and one to guard the flanks if there is a second bridge. The rest an even mix of Pavise Arbs and Longbows. I first clear out the missiles by sending moving my longbows and P-arbs close in, as soon as a missile unit moves in range to fire I put all of my fire on it, and it falls back, repeat as needed. Then I can focus on the infantry. I move the P-Arbs up onto the bridge, and put the longbows on the banks. As an enemy unit moves in I hit it with all my missiles. It wears them down. I advance and retreat one missile unit across the bridge, with all the others on standby to fire. As soon as the enemy unit gets in range I hit it with everything that I have. I stop the retreating unit and let it fire into the enemy too. This chews up a lot of enemy units pretty badly. I try to group my missile units so they run out of ammo in little bunches, as soon as they do I send them off and bring on reinforcements. Eventually I have a full compliment of horse and infantry on the field. I break off the cav and ride it around to the second bridge and get it across, once it is across, or about to be engaged I send all the infantry across the first bridge. It works pretty well. Casualties are a little higher than I would like, but that's the danger of attacking a bridge province.