A bounty cannot be offered, if not after two days the question has been asked. I take the user is anticipating he is willing to put a bounty for the question, and he will do it when he is allowed. Probably he is anticipating it is difficult for other users to give an answer, and he thinks users need an incentive.
I understand that you think the user could be promising something that he is then not going to give, but I think that who is really interested in getting the bounty will wait to see if the OP is really going to offer a bounty; who is not interested in the bounty is going to answer independently from the bounty really being offered.
What I would do is removing that part of the question, as knowing the OP is going to offer a bounty is not information necessary to answer the question. At worse, that information is "damaging" the question, as users could wait two days to see if effectively the bounty is going to be offered.
There is nothing on Stack Exchange that says you should not make public your willingness to offer a bounty, but it's someway contrary of the bounty's spirit: You should not ask a question with your mind set to "I will offer a bounty"; you should ask a question thinking of obtaining an answer.
Only if nobody answered the question, and you are really interested on the answer (or it is someway urgent), you should consider offering a bounty. That is the reason why there is a limit of two days to respect before to offer a bounty: If the question is answered before two days are passed, the question was not that difficult to be answered. (Although, it could be users are trying to guess the answer, but that could mean the question is not well written.)
TL;DR: I would rather remove that sentence about the OP's willingness in offering a bounty from the question.