When awarding existing answers, people sometimes forget to add the link to the answer they're awarding (or they might not know how to do so if they're not familiar with Markdown yet). Because of this, it would be very helpful to have an optional field that lets you add a link to the answer that you're going to award the bounty to (only for this specific bounty reason, of course). Thus, people would see the exemplary answer in question and upvote it.
hyper-neutrino also suggested that the answer to be awarded could have an indicator that it is going to be given a bounty. They also suggested that the blue
+x element showing the bounty amount could link to the answer being bountied.
If this is implemented, another thing that could be done is automatically award the answer based on the link if the person who started the bounty doesn't do it themselves by the time the bounty expires.
To avoid people accidentally copying the wrong link, the field for the link to the answer could perhaps be made editable, although that would probably take a lot more work.