Does the Bose offer a hard wired cord from the device? Or is there a patch cord that plugs into a female connector on the speaker end?
I suspect RRFS is thinking of the latter, where you would replace the Bose cord with the other cord, creating a simpler connection. But if it's hard wired then you are right--only a female->male adapter would work, since you are trying to get a different female jack to plug into.
As I said, I do expect something more is going on, though if this solves it you may not worry about that. The only reason I would try to keep running down the issue would likely be if either or both devices (the Bose speaker system and the Air) are still under warranty. One of the two appears to have some issue, and obviously it might reappear later in another situation, so in that case it might be worthwhile to get the "bad" device serviced or replaced with one that is within specs.