Crossing bridges

[aligern]

Napoleon disliked river lines as they are so easily passed leaving a force defending a bridge outflanked and maybe surrounded. If you had to do it then he believed in bridgeheads (tetes du pont)  so that the defending force could move out aggressively against an opponent and be entrenched .
A unit on the bridge has a considerable vulnerability on its unshielded flank from archers on the bank, so the bank must be occupied. In The Gothic War I think there are three examples where bridges are defended by towers and IIRC all fail because the opponent can get shooting on them from 180%.

Roy

[Erpingham]

Medieval armies spent a lot of time tackling defended river crossings.  Very rarely did they assault bridges (Verneuil is one example, Boroughbridge another).  The trick was to ford elsewhere with a flanking force while pinning the enemy at the bridge (which was done in close proximity to the bridge in these cases but could be done further away).  Actually holding the bridge was not always the tactic for the defence.  Standing ready on a suitably advantageous spot, ready to attack the enemy when part of his force was across, could be effective (e.g. Stirling Bridge).