If I were to set a bounty on a question, could I then answer that question and award myself the bounty to regain that reputation? If that answer was purely to regain that reputation that could be a problem. This is a purely theoretical question and I am not thinking of doing it myself.
No, you can't earn back your own bounty. This is covered at meta.stackoverflow.
My favorite explanation is an analogy:
It's a non-refundable plane ticket. You paid for one (50 of your own rep), the system will throw in a free seat (the other 50 rep points).
If nobody turns up with a valid passport (in this case, an answer with at least 2 upvotes), the plane will still take off. Just that nobody will be in those seats.
You can take the seat yourself (answer and accept your own question), but you're still not getting the refund.