Bairstow must have something on the selectors, I seriously don't understand how he's better than Ballance/Carberry - It would also be one less player for the 'Professional Yorshiremen' Vaughan and Boycott to keep harping on about!
I think its close between the two Bs and Carberry's age (and possibly health issues) mean he is a less likely selection.
The case for Bairstow's defence - he has average mid 40s whilst keeping in the Championship, and has consistently played innings of character - he's always the lad who does it in a run chase or when we're 20-3, and he evidenced this against the Yarpies last year. He has not been best treated by the selectors - after that Test he played very little cricket whilst racking up the air miles for eight months, and he struggled a bit to get back into the swing. He has not done badly against Australia either - no worse than Cook, Trott and Prior for a start - and is the likely long term successor to Prior.
People might baulk at the last bat - believe me, I'm one of them, because Jonny's keeping has never been, for example, at the level of his old man's. But England are obsessed with the idea of like for like and, as a counter attacking batsman at seven, they will hope his keeping improves as Matties did in situ.