Looks like a tight snap (or 2 snaps) would work better than velcro. Or a smock-type bib with velcro all the way down the back. Looks like sleeves would help too. Found these websites with discussions on the topic:
https://community.babycenter.com/pos..._cant_take_off
https://www.mamapedia.com/article/bi...-cant-take-off
http://www.essentialkids.com.au/foru...be-ripped-off/
Edit: Note there is a caution about making bibs too hard to remove, as they can then become a strangling hazard. Probably not as much of a problem for a 3-year-old, though; more of an issue for babies.