If you're bounty hunting, it's a hazard of the job to get charged with murder occasionally. That gets you notoriety that lasts for two hours of gameplay, plus it puts a bounty on you in the system where you got it.
Dealing with this is no problem. The moment you see the charge come at the top your screen and "wanted" appear in red over your fuel gauge, you should boost away from the scene of the crime and get into supercruise and/or jump to another system. You don't have to do that in a Haz RES, but you should go to a new system as soon as you leave it. Once you're in a new system, you can find a new RES to work in until the notoriety has gone. Nobody will be interested that you're a criminal from another system, except that you might get an occasional bounty hunter with a kill warrant scanner, who will want to kill you for the bounty. Unless in an anarchy system, do not shoot them until they shoot you first otherwise you'll become wanted again. Once they shoot you, they become wanted, so you can legally kill them
I normally bounty hunt in LTT 15574. When I become wanted, I jump to Kremainn, Brani or Freng, all of which have very busy RESs, and all are under Zachary Hudson's control, so if you sign up with him and deliver 100T of his stuff, you get at least 20% extra bounty money. He's no.4 at the moment, so until Thursday, you'll get 20% extra. A. Lavigny-Duval is number 2, so if you sign up with her and hunt in her systems, you'll get 40% extra bounty money. These are the only two that give bounty bonuses.
Another thing you could do if the rings have one or more HAZ RESs, like in LTT 15574, is leave the high RES and jump into the Haz RES, where, generally, nobody is interested in your criminal status, but always check that your targets are wanted because you might rarely see clean bounty hunters or even police there. Don't forget when you run out of ammo, that you can't go back to the station. You'll have to jump to another system.
When the notoriety has gone, you can clear the bounty and your criminal status at the IF.