If you are using a bounty, then you're not going to be able to prevent attention on the bad answer(s); that's not what bounties are for. They are designed for the opposite - to draw attention to a question for up to one week. Anyone coming to the question will be able to participate as much as you were; upvoting content that is helpful and high quality, downvoting content that is not, etc. It does not make sense to want to prevent users from participating in the way that you already did on a certain question; we should be careful when talking about user behavior with regard to participation.
As for drawing positive focus and attention to the answer you want, you get to write a custom reason for your bounty. I just did this myself for another question where the accepted answer was flat-out wrong and there were other, better answers with lower scores. I mentioned as much in the bounty text, though I didn't specify exactly which answer I thought was the best one.
On the subject of continued attention where you don't want it because of the bounty's time period... you can manually award a bounty after 24 hours. You don't have to wait the whole 7 days+24 hour grace period. This obviously will end the attention notice to the community for the good answer, but it will also ensure people don't continue seeing the bad answer in the same fashion.
It may seem less than ideal to end the bounty (and the extra community attention) early, but keep in mind that you just gave the post author a total of 60 reputation all by yourself (50 for the bounty plus an assumed 10 for an upvote). That's equivalent to six people coming along and voting up the content, which is a great boon, and not something you can manage by yourself in another way without violating site rules. Even if my answer didn't get upvotes from any other people, I'd always be pleased that someone thought my answer was so good that it was worthy of a bounty, whether it was 50 rep or 500.
Outside the bounty function, the best way to promote an answer is off-site, as there is not really an on-site function to promote specific answers (that's not how the site is designed). There is a built-in way to share content off-site:
Click the Share option below the answer:
You can either post the link to a social media site like Facebook, Twitter, or Google+ (those are included as one-click options by the mechanism itself), or you can post it to a discussion board somewhere like Reddit. Using the Share link comes with the added bonus of earning you, the sharer, a series of badges - Announcer (bronze at 25 unique visitors), Booster (silver, at 300), and Publicist (gold, at 1000). Note that the only way to earn these badges is to share a question or answer using the URL provided by the Share mechanism, which includes a URI fragment containing your account number in order to link visit credit to a person.