Although I initially started on ST mainly as explorers, recently I've been finding that my playing style works quite well with bounty hunters. So here are my tips as far as bounty hunters are concerned:
When you first start off, DO NOT take assassination contracts. Yeah it kinda sucks, you're a bounty hunter yet you can't actually play like one, at least in the beginning. But the thing is, there are a lot of powerful criminals out in the Quadrant, and you are their mortal enemy, so until your captain has "grown his space legs", so to speak, you're just target practice for them. So you want to give your captain a bit more time to build up his bounty hunting skills before you start taking on any actual assassination contracts. I would even say play delivery boy until you have positive rep, a trade permit, and rank (usually rank 1 is enough) with at least 2-3 factions before you attempt assassination contracts. Well, maybe it's OK to start earlier, but it's riskier, and since it sounds like you're having trouble getting a BH going, staying on the safe side is perhaps your best bet.
This doesn't mean that you're doing nothing else while playing delivery boy, though. During this time, besides the obvious goals of building positive rep, getting trade permits / rank, getting your finances together, you need to start honing your bounty hunting skills. The first order of business is to up your Pilot skill. The BH class starts with very low Pilot, which is no good for bounty hunting, because what good is your assassination abilities if your targets can simply outrun you? So for starters, if you've unlocked any starting ships, try to start with one with a high engine-to-hull ratio, the higher the better. A fast/fast rating is best, though medium speed is OK as long as agility is fast (you need high agility in order to catch up with your targets in battle). A medium agility ship
might be OK if your Pilot is high enough, but NEVER fly a slow-agility ship as a BH. Your targets will laugh you off the battlefield. When you can afford it, buy upgrades that add engines (and sails, if you'd like to also keep WF usage down, but that's secondary; the main thing is to make sure your targets can't get away).
Second, I find that boarding works pretty well for BH's, so work on your strength/warrior. Before you write this off as not your playing style, I'd like to say that my BH captains often just use guns (sometimes even torps!) to disable their targets, even though they're built for boarding. But the point is, they
can board and win if necessary, or when it's simplest to do so. When you find yourself facing a high-level target, being able to board in spite of your ship being weaker than his, is a big plus. Now in order to board, you do need to level up tactics somewhat too -- having maxed out warrior/strength doesn't do you any good if your boarding party can't even get on the enemy's ship in the first place. So I'd usually try to level up pilot/warrior more-or-less on par, and tactics trailing behind (maybe 1/2 or 2/3 of pilot/warrior). Having moderate Tactics will give you the option of just torping / gunning the engines of the target when he's low level or roughly on par with you -- to avoid inevitable ship damage / crew loss during boarding. Stealth can be helpful as well in the early game, but you don't need to spend too many XP on it.
In the meantime, if you meet hostile pirates and they don't look too dangerous (i.e., same or lower level than you, lower engine/hull ratio than your ship, etc.), do some target practice. I like to always close in during battle so that the enemy is less likely to escape, so usually I advance, optionally with an initial torp (Cadar greeting
), then gun. If I'm doing good damage, I may gun for a few more rounds then close in and blast the engines out. If I'm not dealing good damage with guns, then I'll go in for the boarding. Don't salvage the pirate ship afterwards, so that you don't lose rep, but looting / rearming is fair game IMO.
Anyway, the main point is to do target practice without risking failing a contract, and getting to pick your targets too. How well you do in battle against pirates will give you some indicator of how well you'd do taking out a real assassination target. Perhaps you'll find that you need to improve Pilot more, or Tactics is too low, etc.. Or maybe you need to upgrade your engines more so that they can't get away so easily. Or buy some weapons to improve your boarding performance. Use pirates as target practice to get your act together before you commit yourself to a real contract. Preferably, you'll do this with pirates of a faction you have a trade permit with, so that if things start looking bad, you can surrender without being looted / executed. Before engaging in battle, make sure they are not protected by an alliance, so that you don't lose rep (though when I play, I usually don't care because the rep loss is relatively small as long as you don't salvage the ship).
Once you're reasonably confident that you can take on a real contract, the next thing to work on is your Tactics / Stealth so that you can do Surveillance efficiently. If you play it right, usually by the time you can take on assassination contracts you should already be able to do surveillance effectively; but just in case, before you sign the contract, try doing a few rounds of practice surveillance on a faction you have high rep with. Surrender if you meet a military ship. If you lose your permit, just land and buy it back. (Make sure your rep never drops below 4, though! You don't want to end up being the faction pirates' target just because of some silly surveillance practice!) Do you get very high success rate (preferably 99%)? If not, you need to work on Tactics / Stealth, and perhaps buy some Electronics to help you out. Hire a Spy officer. While you
can do BH contracts without relying on Surveillance (I've done that, and not infrequently), that kinda defeats the purpose of playing the BH class, since this ability is extremely useful.
(And BTW, this is why in the early game you should be playing delivery boy sucking up to the factions: you want to gain enough rep "buffer" so that you can do these target practice / surveillance practice runs without your rep dipping into the red and military ships and other BH's coming after you.)
Now you're ready to do real BH work! So start taking on those assassination contracts and cleaning the Quadrant of criminals! When first starting out, I'd recommend avoiding Capture contracts until you're reasonably confident that you can capture ships reliably without obliterating them. Fortunately, your Surveillance skill helps out with that:
Generally, try to space your contracts out enough that you have adequate time to hunt down your prey, instead of needing rush from one target to the next. The reason is that given adequate time, your special Surveillance ability can help you fill your contracts without any rep loss, or with only minimal rep loss. When you first arrive at your target's location, always run Surveillance first to pick up his trail. (Make sure you actually picked it up; if your surveillance success rate isn't 100% sometimes it may take more than 1 try.) Then engage him. But don't rush into battle! Take a good look at his ship and faction. Is it a faction you're OK to lose rep with? Some targets are chameleons; they change their flags every attempt. So if it's the wrong faction, just acknowledge/ignore/surrender, surveillance again, then engage again. The best is if he's on a pirate ship (preferably of a faction without any alliance -- but sometimes it takes too long for that combo to come up, so you have to keep your eye on how much time is left for the contract). Then you can kill him without rep penalty, or only minor rep penalty. Avoid engaging merchants. Military ships are OK if you don't mind losing rank (and having to buy it back afterwards). If you're doing a Capture contract, you can also use this ability to wait until he's in a relatively sturdy ship (high hull/armor) before engaging -- so that his ship doesn't shatter to bits before you have the chance to arrest him and bring him to justice. As a BH, you're an opportunistic hunter, so don't just charge into battle. Track your target first, and "play with your food" until he's in the best ship/faction combo before you go in for the kill.
After the battle, if you've lost any permits / ranks, buy them back ASAP. You want to be feared by the quadrant's criminals, not to be hated by factions who have armies backing them up. (Well, in theory, anyway.
Once you've established yourself as a fearsome bounty hunter, you will have more options open to you, such as targeting a particular faction just for the fun of it, etc.. Or go for the Independent Captain award and shoot every moving object out of the sky. Hopefully by now you have a roadmap of sorts of how to get to that point.
)
), then gun. If I'm doing good damage, I may gun for a few more rounds then close in and blast the engines out. If I'm not dealing good damage with guns, then I'll go in for the boarding. Don't salvage the pirate ship afterwards, so that you don't lose rep, but looting / rearming is fair game IMO. 
Anyway, the main point is to do target practice without risking failing a contract, and getting to pick your targets too. How well you do in battle against pirates will give you some indicator of how well you'd do taking out a real assassination target. Perhaps you'll find that you need to improve Pilot more, or Tactics is too low, etc.. Or maybe you need to upgrade your engines more so that they can't get away so easily. Or buy some weapons to improve your boarding performance. Use pirates as target practice to get your act together before you commit yourself to a real contract. Preferably, you'll do this with pirates of a faction you have a trade permit with, so that if things start looking bad, you can surrender without being looted / executed. Before engaging in battle, make sure they are not protected by an alliance, so that you don't lose rep (though when I play, I usually don't care because the rep loss is relatively small as long as you don't salvage the ship).