I would question whether it's an abbreviation for "A Bastard", since the A is followed by a colon ("A:"), showing that it's an abbreviation, which the indefinite article "A" clearly isn't.
I accept that A:B. might well mean illegitimate, and if all families where this appears have a couple with different surnames that would be good evidence for that. The opinion of Durham Records Online is also worth noting, since they have a lot of experience of these documents, but I still don't think that explains exactly what the letters stand for. I was thinking it might be A.... Born, but I can't think of a suitable word beginning with 'A'.
(The other thing that crossed my mind was that it might be Anabaptist, so referring to someone coming to the C of E after an association with them, but if all the couples appear to be unmarried, that's probably unlikely.)