Is it appropriate to use a bounty to say 'thank you' for an already-supplied answer? Will the site let you assign a bounty to an answer that exists at the time you read the question?
Yes, this is definitely possible. When you offer a bounty, you get to choose from a number of possible "bounty reasons", with one of them being
Reward existing answer
One or more of the answers is exemplary and worthy of an additional bounty.
There is a 24 hour waiting period, but then you can assign the bounty to whichever answer you choose.