Control of bridge

[Coniglius]

Many game systems define control of a hex as 'undisputed'. In order to be 'undisputed' you would have to occupy both entrances tot he hex (either side of the bridge hex). If you occupy one side and the enemy occupies the other, then the hex is considered to be 'contested' which means control is disputed. For your scenario, I would interpret control as having uncontested (undisputed) control of both entrances to the bridge. You may even want to expand that to include having the adjacent hexes clear of enemy forces as well. This might increase the likelihood of friendly casualties, but such is war.