The Faction I fight for currently has no station of any kind, so I did hand in the combat Bonds at the surface port of another faction and not in one of the outpost controlled by the enemy. What I can see is that for one of course the influence of the faction I fight for goes up, but also the influence for the faction that owns the port where I hand them in did go up a bit.
Traffic report did only show one other ship, probably just somebody passing through. I'm pretty sure the faction owning the station where you hand in bonds does benefit from it a bit, alltough the rise of influence of the faction I fight for was higher then the rise of influnce of the faction owning the port, so it should outweight it.