There are several different types of bounties, and in yer case, you sound like you have a "hard bounty" which, if you check the Nav Panel under Transactions, will tell you what kind of bounty it is, if it says a time limit of 6 days, then you either have to wait the 6 days for it to go dormant, then wait another 6 days for it to turn into a "Legacy" fine, then you can pay it off. During dormant status, you can't do anymore bad things in that system, or it turns into another 6 day Hard bounty, and you can't get "scanned" by any ships associated with whoever gave you the bounty. You can't pay off a 'Hard" or "Dormant" bounty, you have to wait for the time limit to expire. When it finally turns to Legacy, then you can pay it off at any Interstellar Broker.
The 'Suicide' method is quicker if you need to stay in system, or frequent the area. Buy a sidewinder, strip it down to nothing, fly around the issuing authority area til they scan you and obliterate you, that removes their issued bounty only, and you pay the fine with the rebuy.
Now, there is a 'Short' bounty, whereas you are bounty hunting and accidently shoot an unscanned ship or a clean ship, if you only fire once, you immediately turn 'wanted', but there is a short 8 minute timer on it, you need to immediately vacate the area, do not kill the 'clean' ship that is firing back at you, cause then you will get a 'hard' bounty. If you leave the area before that ship is killed (others in the area may be firing on that ship), then you will not get the 'Murder Warrant' associated with you. The 8 minute timer will countdown and it will then say "H-jump" which means the 'wanted' status will clear the next time you jump to another system, then you can jump back to the system and pay off the fine associated with the accidental misfire. Now if you fire on a 'clean' or 'unscanned' target, and do enough damage before you depart, then it turns into a 24 hour 'Hard' bounty, even if the 'unscanned' ship turns out to be 'wanted' itself, you can then kill the target without repercussions, but you will still have to wait the 8 minute timer to clear your 'wanted' status.