I've been around this game for over two years, and some of this info I just learned, so forgive me in advance, but I'm going to over explain this. If any more experienced commanders see me post something wrong here, feel free to interject.
If you get a bounty on you, you should find your nearest Interstellar Factions. These can be found in Low Security Systems.
1. Go into your Galaxy Map, and hit RB until you get to the fourth tab, which has three options at the top: Realistic, Map, and Powerplay.
2. Below that, it will say Map View Configuration. You can change this to different options, so select "Security".
3. Once you do that, more options will appear below it. Make it that only "Low" is selected. All that should be left is Low Security stars.
4. Pick a star, and travel to it. Any station there should have an Interstellar Factions component. You can pay off those bounties there.
Again, sorry to over explain, but I only just learned about sorting by security levels. The information isn't exactly easy to find if you don't know where to look.