Slide it, Man!
In your "impossible" transition, I'm assuming you are already fingering an open A chord. The 2,3 and 4 fingers are in the same position as the B chord, right? Just two frets down (toward the nut). So, just leave them in position and "slide" them up to fret 4, then as they come into position plop your index finger for the barre.
This will be a faster version of:
So, when I need to play B major, I first put the fingers 2, 3 and 4 down, and then add finger 1 (bar).
You said this is slow, but maybe it will be faster if you don't even lift up 2,3 and 4, just slide them. As you slide, start to move the barre finger into position as well.
To Practice:
Finger the Bmaj barre chord on every fret, going up and down, but don't lift up your fingers, just release pressure and slide them around the fret board: B, C, C#, D, E (you are barring the 7th fret on E)...as high as you want to go. Also slide "down" the fret board until you are on Bb (barre on fret 1), then lift the barre and slide 2,3 and 4 into position, and you have an open A chord! Practice the transition between open Amaj and Bbmaj (1st fret) barre over and over.
Basically you slide the fingers, which are firmly in position (because you practice and get muscles!) along the top of the strings and just squeeze when you reach the target fret.
EDIT: Advanced Note
As an advanced point, take note that the open A chord and this B chord are the same "form". That's right, except the nut is functioning as your barre. As you slide the form up and down the neck, you change key but keep the voicing, or form. The form is "A" in the C-A-G-E-D school of thinking, named after the open chord. So what I am really asking you to do is to practice your open "A" form all over the fret board.