Now that you can put a bounty on someone else question. It would be nice to be able to attach a comment to the bounty, to explain what you expect opening it. For me an important motivation of offering a bounty is that I would like some overlooked aspect of a question to be explored. It's easy to explain it in the question for your own questions, but on someone else question I feel it would be better to explain what you expect offering more exposure to a question.
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This is now completed, you can add a custom bounty message at the end of the start bounty process:
see also: How should bounties be categorized?
I disagree with this feature. The purpose of the bounty is explained in the faq.