I think it would be useful to have all the answerers notified when a bounty is initiated on a question to which they have previously answered.
If it's too many notifications, then a per-individual setting may be set to opt-out.
As animuson noted, a per-user setting is almost certainly not going to happen because SE tries hard to avoid having any settings as a design principle.
Setting that aside, a bounty implies that the current answers are inadequate --- otherwise there's no need for a bounty. Given that, notifying current answerers might even be undesirable. Yes, they know the question, but they already gave an inadequate answer to it so why ask them again?
If an answer were close to being right, but not quite, presumably the asker would notify the answerer via comments instead of placing a bounty.