When I make my bibs, I use terry cloth on the bottom (because it is so absorbent). I like flannel on top (I like them to look nice and fun), but I use ripstop in the middle (the ripstop help your fabric absorb without allowing it to absorb all the way through to the clothing). The ripstop helps keep the bulk down, so it's not as much like a little kids bib, and they can be washed and washed. I'm sure others will have will have other helpful hints, good luck

My sewing group made bibs out of terry cloth hand towels. We got them on sale at Sears. The care home asked us not to use velcro because if it isn't fastened it snags everything in the laundry. They said they don't have time to forget to fasten the velcro when they take the bibs off. They asked if we could put ties but instead of making them so they tie they asked if we could sew some snaps on them and space them apart to make them adjustable. They said if a patient pulls at it it will unsnap and if it's tied the patients may try to pull it off over their head, get frustrated or freak out because they can't get it off. The facility is home to many dementia patients and they smile and appear to look happy when we deliver the colorful bibs and spend time visiting with them.

I use a Terry hand towel and add a yoke to the top or you can cut off the top of a shirt to add.

I just suggested this to a friend, use terry kitchen towels and get a few clips for bags, like you use for potato chip bags, and just clip the towel to the shoulder area of their clothes.

When I made them for Fred (step father) and mom I used hand towels, cut a circle on one end and used binding and left a tail. Easy, quick to make and wash great. If needed your can make a pocket at bottom with a little material, and if backing is needed a shower curtain liner can be attached easily.
Velcro can be used but to much stuff can stick to it then you have to pull it off to use it.

Lots of good ideas here, but the velcro near the neck isn't that great as it can pull their hair if not put on correctly. I think ties or buttons with tabs are better for the wearer.