Cooke's 'Mastering the Scales and Arpeggios', from 1931, came recommended to me as the one-stop reference for learning to play scales. On page 27, I find A-flat. The text says, 'Right hand: Fourth finger on B flat'.
However, the fingering given on the staff at the bottom of the page starts out 2-3-1 instead of 3-4-1, thus alternating between 3 and 4 on b-flat. This is like nothing else in the book, and there's no mention of it in the prose. So I think it's a typo, but I wonder if there's some good reason that's escaping me.