I have used:
Cotton/cotton (always two layer bibs)
cotton/terry cloth
cotton/sherpa
cotton/minky
terry cloth/terrycloth
cotton/cotton with inner layer of waterproof PUL
Cottton/bottom layer of PUL
there are tons of ways to do it

You can close it with velcro, a button, a snap. I like to do velcro with the understitching hidden when its a gift