An intrepid OT teacher ponders the ethics of bribery here.
I would tentatively suggest that the situation is less complicated. By bribing a border guard you can claim no complicity in the corrupt system. If you tried to bribe a immigration officer in Heathrow or Auckland Airport you would find that the system is not influenced at all by your bribe. Equally your refusal to bribe a corrupt guard would do little to change the corrupt guard or system. Rather than a consequence based ethic how about a virtue (character based) ethic.
What sort of person bribes a border guard? If you are bribing him to allow you to smuggle narcotics or children for prostitution then your bribery is motivated by avarice and lack of concern for others. Your bribery is bad because you are bad in motive. If you are bribing him because of your compassion for a refugee from a corrupt and despotic regime your bribery is good, because it is motivated by your compassion. Bribe for the glory of God! (Of course accepting bribes is a different matter altogether.)
Then there is alaways Proverbs 17:8, :-)
Now thinking about the ethical problems in marginal situations has made me think a of a trickier example. Anti-slavery groups often debate whether or not it is ethical to buy slaves their freedom. On the one hand you are showing compassion to the individual (virtue) but on the other hand you are fueling the slave trade by becoming a buyer (consequence).
Let me know what you think :-)