He can fool the BO if he change his personality and disguise as another person
BO wont suspect Okiya as Akai since they already saw in their own eyes that Akai died
so there is 50% possibility that he can fool BO
I think they did not meet Bourbon when he joined and waited for the right time to appear in the BO
so I say Conan gave Akai a voice changer and Akai called the BO and asked if he can join and agreed
then at the time he was assassinated he jumped out of his car and disguise and came to the BO