After trying to explain Double Bribes in-game to someone, I decided that there needed to be a tutorial on the forums that we can easily redirect people to so that we don't have to tediously explain it in-game.
It should be noted that Rephacks relative to the ID you're using may influence your diplomacy with factions. For a list of these Reputation Hacks, check this website.
Step 1 - Location, location, location.
Firstly, we have to decide what faction we want to have at double bribed. In my instance, I'll be targeting the Liberty Police Incorporated NPC Faction. It is important to note that if your reputation with the faction is borderline green with them, you won't be able to find any bribes for them. In my case, the LPI currently have a '"positive-neutral" stance:
If you use FLStat, you can find locations that sells the bribes you need.
Step 2 - The Bartender
To start, walk into the bar and approach the Bartender. He will most likely either have a bribe or a rumor. If the bartender has a rumor or unwanted bribe, hit F1, go into 'Select New Character', re-select the character you were on and re-check the bartender. Continue doing this until you get a bribe for your desired faction.
Excellent! Now we have the bartender in on our devious plans! Now we can leave and return the bar, letting other NPCs cycle, but leaving the Bartender.
Step 3 - The tough part.
Now we have to get an NPC that will offer us an LPI bribe too. Goto the Equipment Dealer/Commodity Dealer/Ship Dealer and then head back to the bar. All of the NPCs will have cycled through, but the Bartender will still have the required bribe. Search the NPCs for a bribe. If you don't have an NPC that has the correct bribe, visit a dealer on the station and return to bar. Continue as necessary.
This is the part that will trial your patience. Keep being persistent and keep trying until you have the two required bribes.
Now that we have the two required bribes, take both of them, then check your reputation. It should look like this:
You can now purchase that ID, or /droprep until you get this as your desired IFF.
Practical Uses.
The really good thing about Double Bribes is that it quickly allows for people to change their ID and IFF and it also has a strong positive effect on the corresponding Guard Faction.
And that's it! Double Bribes may test your patience in may scenarios, but keep at them, despite the mundane feel about it all.