Since the bridge is a footbridge I would connect the end of the bridge to the nearest highway with a footway showing the shortest route somebody on foot would be able to walk.
Obviously if you cannot get on foot to the highway because of safety barriers or other obstructions you shouldn't join the footway to the highway there
there, likewise if there is no sidewalk or any restrictions on pedestrians walking on/along the highway you shouldn't join them.
eg like here [http://www.openstreetmap.org/#map=19/53.96654/-1.09225][1]
[1]: http://www.openstreetmap.org/#map=19/53.96654/-1.09225