I haven't been playing long but I have come across my fair share of small bounties against me.
I fly with turreted weapons, and before them gimbled and I have set my ship up so I can fire constantly. Because of this occasionally the feds will get between me and my target and... They do nothing. I have watched their Shields light up but, I believe, because they weren't targeted they are OK about it as they were glancing shots, not sustained fire.
The only times I have had a bounty on my head were due to lack of patience and not paying attention. The first was not waiting for a scan to run fully before I engaged a wanted target (it was obvious it was wanted as it was being engaged by the feds and firing back). The second was where I was attempting to target a wanted ship I had previously scanned but somehow I manged to target a none wanted target and I opened fire. My turrets had almost dropped his Shields before I realised.
Anyway, as others have said, avaiding in these situations is easy. It's a short time limit on the bounty usually, I have seen 8 minutes, but someone up there said 10 so it could be that and I was just not looking in time.
Avaiding is simple, as soon as the bounty prompt pops up you will notice it says 'wanted' in the bottom right. In these situations throttle to the blue 'handling' zone and turn away from the feds, if you are in a mass locked area (like a ring) point away from the rocks and out of the ring at the same time. Now hit the afterburner and firewall the throttle.
While I am turning and burning I retract my hard points and max out my engines, then I take the last remaining pips out of weapons and put them on shields. You aren't doing anymore fighting now, so there is no point wasting the pips or slowing down your exit. Depending how it's going you may wish to move power to the Shields over the engines, but you must keep some power going to the engines so you can keep bursting and keep your acceleration up. If you are in an asteroid cluster use them to give you cover, put them between you and the feds, but keep your speed up and maybe through in a sliding corkscrew manoeuvre to make it difficult for the weapons to lock on.
Once cleared of mass lock jump to lightspeed as quickly as possible, it doesn't matter where you are going. You may wish to unlock a location target before you clear mass lock just in case it wants you to align with it.
Once you are out of danger bring up your galaxy map and target a station in another system, orientate and then jump. Once at the other station dock and redeem any bounty (etc.) you can, just in case. Then wait the timer to run out (listed on the left panel under transactions I believe), and then jump back into the previous system and head straight for an outpost. I went to a station in the previous patch and wasn't shot, but outposts are less picky so maybe don't risk it.
Now dock, pay your fine and you are good to go again. Maybe check if you can claim any more bounties (etc.) and then move on.
