I have asked a question and put a bounty on it. Looking at the 2-3 answers, it seems there might be a bit of confusion about what exactly I am looking for in the answer. If I add an edit to my question, to clarify it a bit, do the people who have answered get notified of the edit, or will they find out I have edited ONLY if they happen to read the whole question again?
No, answerers do not get notified about edits you make. The only people that get notified about edits are those who follow your question.
In general, there should be no need for such notifications. Note that you should not make edits "in response" to answers, in particular if these edits invalidate existing answers, see also this recent meta thread. If you have follow-up questions provoked by the answers you receive, ask a new question instead.