To melee
1) Click on the bridge hex.
2) Go to the dropdown menu under "Melee" and choose "Begin Melee"
3) The melee symbol should appear above the bridge
4) Click on the attacking unit and hit "add to melee"
5) Resolve Melee
To bombard bridge:
1) Choose arty unit that has LOS on bridge.
2) Choose Fire mode.
3) Rightclick Bridge Hex.
(Note, the small bridges over creeks cannot be destroyed, only bridges that take up full hexes)
I just checked both of these in Corinth, to be sure my memory was right.