Well, you could get that bounty from attacking a clean ship most probably. There is a bug FD has acknowledged and said to be working on where law enforcement will start attacking you for no reason. If you retaliate you get an assault bounty and become wanted. They said for now we should not retaliate, but jump out and back in. Until they fix it. You can also get fined for smuggling and perhaps unauthorized access, loitering, etc.
In any case you should be able to figure out who wants to be paid by looking at the thing in the transaction list (something like "fine in federation", that means any federation-aligned station will take your payment). Then head for the appropriate station and under one of the options in the "contacts" submenu you'll see the option to redeem yourself.
Thanks for idea's, but issue is that I've got no fines, There is no option in contacts to pay off a fine or bounty.
I've cleaned up my act and have not been scooping cargo left floating around
I also tried killing 'wanted' ships thinking it might help my rep, but that seemed to make it worse.
I'm just confused as I'd like to clear my name with the Fed's.
I did get a mission that seemed to offer the chance of improving my situation, but it's either not worked or had too little effect.