I saw this the other day- it doesn't specifically mention bibs, but I thought it was somewhat relevant:
http://www.safekids.org/our-work/research/fact-sheets/choking-and-suffocation-prevention-fact-sheet...."Each year, approximately 873 children ages 14 and under die from airway obstruction injuries."
Also says: "Common items that strangle children include clothing drawstrings, ribbons, necklaces, pacifier strings, and window blind and drapery cords."
So- can't say for certain either way whether anyone's been strangled by ties on a bib, but that makes it pretty hard to believe that it doesn't happen. (Even in the olden days when people "used ties like they were supposed to", whatever that means.)
To be fair- also can't say whether the statistics would be any different for the velcro or snap variety, I don't know of anyone who compiles detailed records on things like that.
I know this sounds morbid, but that's kind of a bummer. I always like actual numbers, 'cause our opinions on whether something is common or never really happens seem to vary according to whether or not we know anyone it's personally happened to.
For example, I had a conversation at lunch today with a pregnant coworker who thinks drinking alcohol while pregnant is fine because her grandmother did it back in the '40s and all four of her kids turned out normal. Once spending just a few hours taking care of a 4-year-old boy with Fetal Alcohol Syndrome was all it took to convince me that it's not fine.
(It was 20 years ago and his name was John and I've never forgotten him. Hearing her say that today just made me want to cry.)
Experience is subjective.