Why is it a privilege to set bounties? I think that everybody who has a minimum of 51 reputation (because that is the minimal value of bounty), should have the ability to set bounties. It's that user's decision - his reputation, his bounty.
What is meta?
- Any Stack Exchange user can ask a question
- The community provides support, votes on ideas, and reports bugs
- Your voice helps shape the way Stack Exchange operates
Bounty is more than just paying reputation to gain attention.
For one, there is good chance the attention will bring you not only the help you seek but also more upvotes (assuming that's your question, or you set bounty on question you answered) many times 50 rep bounty would give you more than 50 rep in return, hence bounty might be a way to gain reputation.
Also, you can give bounty as a prize to answer you deem extremely good or helpful: such prize could have been called "super vote" and in my opinion this alone is a major privilege.
We need users to understand more about the site and how to be a good community member before we give them the option of offering bounties. It's a matter of trust, just like any other ability on the site.