bib (n.)

linen worn over the breast, especially by children, to keep the front of the dress clean while eating, 1570s, from verb bibben "to drink" (late 14c.), which is perhaps imitative of lip sounds; or else [Skeat] it is from Latin bibere "to drink" (from PIE root *po(i)- "to drink"). If the latter, it is difficult now to say whether this is because it was worn while drinking or because it "soaked up" spills.