While it's important to go after the bounties at the right times, you have to keep an eye on your overall goal: winning. A lot of players will forget this and risk way too much as they try go after bounties. You have to be wary of these players and adjust your game accordingly. You will often have to tighten up as your opponents are willing to play a wider range of hands in pursuit of Knockout Bounties. While everyone else is pushing with a wider variety of hands, you need to play smart and remember not to stray too far from your normal game plan.
Of course, there are times when you should be more aggressive in trying to take down a bounty. If another online poker player at your table is short stacked, by all means go after him, especially in the early stages of the tournament. If you're in the small blind and a short stack is in the big blind, you should force his hand with pretty much any two cards. In this case, the small risk in doubling him up is outweighed by the reward of taking down the bounty.
Inversely, if you find yourself short stacked in a Knockout Bounty tournament, you should be willing to push all-in with a narrower range of hands than you might otherwise play in a non-bounty tournament. Remember, everyone at the table is going to be gunning for you and your bounty, so you want to give yourself the best possible chance of having your hand stand up so that you can rebuild your chip stack. To that end, you should also be more wary of bluffing and of trying to steal blinds with a marginal hand, because you're probably going to get called by at least one player, regardless of what cards they're holding.
In the later stages of these tournaments when you're getting close to the money, my advice is very simple – forget about the bounties and just play your normal game. If you've made it this far, you don't want to make any unconventional or risky moves just for the chance to take down an additional bounty. The risk simply doesn't justify the reward and your chips are just too precious to throw around when first-place could be within your grasp.
So go ahead and gun for a bounty when the opportunity presents itself, but don't go out of your way trying to take another player out just for the fun of delivering a knockout punch. Remember, even in a Knockout Bounty tournament, there's no sweeter reward than to be the last man standing after the final hand is dealt.