"given this measurement and our prior beliefs, the probability of page A being better than page B is X%"

FTFY ;). I think Bayesian methods add a lot of interpretive power, but I'm not sure that it would help people make a correct interpretation. I suspect that if practitioners are neglecting the difference between a one-sided and two-sided test, they will likely forget (or gloss over) what priors are (and their non-trivial implementation).

I definitely agree that their is a disconnect between the math and its interpretation, though.