Yes, if the bounty expires with no answers with positive score, it goes to waste. And yes, it is possible and allowed to answer the question yourself, but you cannot award a bounty to yourself, even if the answer is posted in someone else's post. You can get a bounty for an answer to your own question, but only if the bounty was offered by someone else.
In any case, don't worry too much about it: it's only been two days since you offered the bounty, and there are five more days left. It is not unlikely that the question will get an answer in the next few days. But even if it does not, there is nothing you can really do: the reputation will just go away. This is one of the factors you have to take into account when you choose to offer a bounty: you must be willing to let those rep. points go away if there are no good answers after the seven-day period. That's just how things work.
So my advice is: if the question gets a good answer, award the bounty to it (but please don't award it to a bad answer just so that the points don't go away). If it does not get a good answer, forget about it and move on.