You will have worked some of this out or read it by now, but just in case here are a few points that I didn't find out straight away...
1/ I find that big ships (and most small ones) scan you before they try and open fire. Make sure your hold is completely empty, that way your fight with an Anaconda that was always going to be right to the wire doesn't end up as "and also with a wing of three Clippers" unexpectedly.
2/ If you accidentally strafe a ship that isn't wanted, you will get a fine and become wanted. At that point, I leave on supercruise for a minute to reset the instance because if the ship you strafed gets blown up by another NPC, then your part in the matter gets you a murderer status which is really annoying to deal with.
3/ Get a Kill Warrant Scanner, and scan any decent sized ships with it before opening fire. That might up the bounty from 40K to 80K (or 120K on a big ship to 200K) which is well worth the time it takes to perform the scan. Sidewinders and Eagles I don't bother with, they might jump from 6K to 12K but in the time it takes to scan a ship I could have shot down two more sidewinders so pickings have to be very slim for me to bother investing the time.
4/ Look out for bounty hunters, the NPCs also attacking pirates. Tag along to a fight they started, it makes things go much faster and with less risk, and you still get the same payout.