Having read the previous reviews before purchasing these bibs, I was a little doubtful about them staying on the carrier, but felt it was better to put up with that than having to wash the carrier more often. However, when I have received the bibs, I've discovered that they actually have an opening at each end that you slot the harness of the carrier through, so there is no way that the bib can fall off. So glad I decided to buy these!
(The carrier we are using with these bibs is the BabyBjorn Miracle, but they state that they will fit other carriers except for the Comfort)