There is one thing that all STW players fear, and that is a bridge province. There are a few things to always keep in mind:
Early Game Offences:
The early game would be in your first years as Daimyo, your army will mainly consist of Yari Ashigaru, Yari Samurai, and Samurai archers. An army attacking a river province should consist of (this is only my recommendation):
Now that your army is assemble you should wait, if it possible, until summer or autumn to attack, since I have found these seasons have the least amount of rain. Once on the battlefield bring your archers up to the rim of the river. If their infantry unit is set up in front of the bridge open fire once you get in range. While bringing your archers up assign your infantry units to get in the order of armor strength, Yari Ashigaru being in the rear and Yari Samurai being in the front. The purpose of this is to get a constant flow of men over the bridge, if this is not done the first unit may rout to soon and your attack will be thrown off balance (remember every second counts in a bridge battle). Many people feel that your first infantry units should be set up in loose formation to lower casualty rates due to enemy arrows, but I have found that by the time your change your formation to tight or wedge the enemy will be upon you. As the enemy brings his units to attack yours have your archers start raining arrows upon them. The enemy will soon encounter your infantry and a mushroom cloud like mob will form at the head of the bridge. Continue having your archers fire at the enemy units. You will notice that you are loosing more Yari Samurai than the enemy is; this is due to the fact that your forces are attacking in a more vertical column that allows the enemy to surround your units. At this point have your Ashigaru units form a wedge formation to break the back of the enemy line, the rush of fresh units will devastate the enemy and boost the moral of your troops. (Don't wait to long to do this, if you do your Yari Samurai will rout.) This second wave of offence should be done after the arrow fire is focused on the Yari Samurai or if you really need the extra kick. The enemy will rout within minutes if your timing is right, timing will take lots of practice. Send your troops towards the archers and mop up the rest of the units.
Mid Game Offences:
The mid game will occur when you have established your empire, your tech tree has grown, and you have a substantial army. Your castle at this point should be around fortress level. I would recommend an army consisting of the fallowing (remember this can vary depending on how much Koku you have):
This offence is not much different from the early game offence. However, you will notice one main difference, shock troops and some cavalry. The cavalry are not completely necessary since they cost a lot of Koku and are not very affective on river provinces until you have the opposite side. This time in the battle you will want to send your Naginata over first. Since Naginata are extremely well armored you should send the first across in a tight formation and the next few in a loose, you will need at least one unit to be in a tight formation in order to get some ground. If you start to find that you are loosing to many men switch to a tight formation. Once you have your Naginata across immediately send your Yari Samurai. Use your No-Dachi or Warrior Monks as you did the Yari Ashigaru in the early game offence, they will be much more effective since they are shock troops. If you feel your men need support send your Yari Ashigaru across and hope they will weaken the enemy moral. Hopefully the enemy will rout and then you send in the cavalry, if you have any. Charge them at the enemies range units. Once your men are at the other side you have pretty much won the battle. Send your cavalry, shock troops, and Ashigaru to finish off the routing troops.
End Game Offences:
You are now one of the last contestants for Shogun. You control most of the map, your tech tree is booming, and your army is vast. With end game bridge battles there is a double-edged sword. Both sides will now have reinforcements. If you move fast enough and have developed skill in river province battles you will destroy the enemy but if you give him time to replenish his forces you will not live to regret it. Armies at this point will be too different from one game to the next for me to recommend a standard army. Just keep a few things in mind for building your army.
Again this offence is not much different from the others except for army size. As always send your armored units across first, then your Yari units, then the shock and reserve troops. It will be much harder to win on a first run so keep your units moral high all the time and hope for a stalemate on the first attack. If you do, by chance, break through the enemy lines send out your heavy cavalry right away then your reserve troops, fallowed by a single unit of archers. If you see that your troops are wavering don't push them and send them back to your side. Check to see if you have any units that have less than 15 men and rout them so you can get fresh reinforcements. If you keep stalemating you will soon be in trouble since time will run out. Send your Heavy Cavalry across to coax some units and then open fire on them while retreating your cavalry. Once you have taken the enemies side send every single troop across and place them in strategically. Your job now will to wipe out any enemy reinforcements that come. Don't feel bad if you loose because of time. As long as you killed more troops than you lost you will be fine. Just keep on attacking until you have the province.
Note: Practice on custom battle until you get the feel comfortable. Don't rush onto a campaign and go way over your head.