For me it depends on the land of the defending side. If its flat on my side and rough on theres i will send a small HC group in then right when they hit call retreat. Some times you can get their cavalry to chase them. them you have to have low angle ranged units(aka muskets... etc) and when your cav are clear of the bridge have some Yari Cavalry and some Nanginata Cavalry come in while the LA range units fire up the enemy cav as they cross and right when they are about half way across the bridge i pull my muskets back while i have naginata and yari come in from the sides while(if i can) i have rallyed my HC to come from the front and attack like that. If you lucky you will get rid of most of their cavalry units. Then if they still have some infantry on the other side move in some YC to distract their archers and move a musket group(2-3 full squads) and start weakening their infantry then slowly move the main stay of your army in( Yari Samurai, Kensai, monks,... etc) and pull ur muskets back when your infantry reach them(to prevent FF) and have your infantry work over the enemy infantry while your yari finally stop pecker wooding around and finally come in for the kill on their archers.

If its flat on the enemy side and rough(preferably very high ground) and set some archers and LA ranged units on the hill side. then follow the same strategy up top but when your units are on the bridge u should send in fodder infantry first and have them hold on the bridge while you work them over with Range.

I hope this helps you all out i know it was fun playing the game to find these strategies.