I don't think that "Sherry hunting" was really Bourbon's mission. The Boss has never officially ordered anyone to hunt down Sherry, so the fact that he/she only decides to do it now makes this whole thing suspicious.
Bourbon didn't believe in Akai's death from the beginning, and not to mention that The Boss and many members from the Org. do not trust Kir. Therefore, in case Kir was really a spy and can inform the FBI any second, The Boss might have spread that rumor in order to mislead her. Since Kir is unaware of Bourbon's real plan, she wouldn't contact Akai and tell him to prepare for Bourbon's hunt.