This is a problem that I have been getting every time I have given some of my questions a Bounty. But instead of GAINING points, as I thought a Bounty should, I LOSE them. What is going on?
Have you looked in the help menu? This page discusses what a bounty is.
When you write a question, but for whatever reason aren't satisfied with the answers you get, you can start a bounty. The bounty is a reward you give using your own reputation to the user that answers your question. Users are enticed to answer the question because if they do, they might receive the reward. In exchange, you get the answer you wanted.
If you want to gain reputation, go to the featured questions page and answer one of the questions. If you answer it well, the person who started the bounty might reward you with the bounty amount.
For more information, see the help page I linked to above.