During a skirmish at an extraction side I accidently hit a security force guy and got a 200 credit bounty for the Federals and was wanted.
I attempted to pay it by flying to a federally controlled station (as I had done in the past in my sidewinder without problems) but was blasted out of the sky in my Viper that I just bought.
How am I supposed to pay off bounties if they kill me when I go to pay them?
You need to pay them at a station NOT owned by the faction you are wanted by. Utilize your system map and click on the stations on that map. If it says "Wanted", don't go to that one. Find one that doesn't say it, dock there and pay your fine under contacts in station services. Once paid, you can then utilize that other factions stations and there will be no bounty reward for your head.