The bounties are a great feature and the idea that they need to be linked to your reputation is crucial, but should they really reduce your reputation?
A simple alternative would be to have reputation separate from bounty points. Every reputation point earned is a bounty point earned, and every reputation point lost is a bounty point lost, but every bounty point spent is not a reputation point lost.
Another user has asked a relevant question: Is using reputation to buy bounties polluting the meaning of reputation?
Reputation is supposed to be a reflection of your contributions to the web site - very loosely a measure of how much the system/community "trusts" you (whatever that means). However, I've noticed that more people these days seems to be viewing rep as a commodity or currency to be traded in exchange for something.
I like this description because it describes what reputation should mean ("reflection of your contributions"), but also what it becomes because of blunts ("a commodity or currency"). The simple solution is keep reputation and currency separate.
One thing I must point out is that I have never made a bounty, so my experience with the system is limited. But a lack of experience is experience: my meager ~1500 rep on SO is precious to me, so I have intentionally avoided giving bounties. But I would like to reward those kind souls who answer some of my more obscure questions.
I imagine that one of the greatest advantages of my proposal is that it helps encourage more obscure questions. Its easy to find answers to popular questions on SO, but obscure ones that only a handful of people experience often go unanswered. They aren't off topic, they just aren't popular, and thus not rewarding to answer. By encouraging bounties, we encourage people asking and answering more good but obscure questions.
Update with some scenarios
A friend of my friend is my friend:
User A answers 1000 questions and earns 100,000 points, greatly contributing to the community. User A has a big problem which no one is able to answer, so he spends 100,000 bound points on 1 question. User B has just started using the site, sees User A's question, provides the perfect answer, and leaps to 100,000 rep in an instant. Is this fair? Yes - because a friend of my friend is my friend. User B has contributed very little to the community directly, but he has contributed very greatly to User A who himself has contributed greatly to the community, so User B has contributed greatly to the community indirectly by proxy.
A flood of bounties
Suppose hundreds of high-rep users flood the site with bountied questions? Is this good? Yes - the more questions the better... as long as they have good answers. Will they be answered? The harder the question, the higher the bounty will need to be to get an answer. So those high-rep users will have to put a higher bounty for a higher question.
What about low-rep users (like myself)? If high-rep users are putting high bounties on questions, who will ever look at the questions asked by users who can't afford bounties? High bounty questions have a lot of competition, so there is still incentive to answer low or no bounty questions to make a modest amount of points for less work.