Will be be able to bribe our way to a better rep/mission with an org/mission giver or bribe a org/mission giver to overlook bad/undesired conduct/actions.
Yes, in certain cases.
Some Orgs/Contacts will have interactions where they would normally act in X way because your Reputation is below X threshold, but they might temporarily overlook that reputation if you immediately give them something. Common example: slipping a bouncer some money to get into a club.
There also are plans to allow you to gain reputation by bringing an Org/Contact something they like (though it should be something more gameplay-interesting than just money). We drew on a few different game types for inspiration when developing the system, and among them were social simulators.