'bib' (verb) ultimately originates from Latin, specifically the word 'bibere', where 'bibere' meant 'to drink'. The noun sense ('bib' as a protective cloth) developed later in English usage to denote a cloth worn at the chest or around the neck.

'bib' (verb) passed into English via Old French and Middle English verbal forms related to drinking (e.g. Middle English 'bibben'), and the noun sense appeared in Middle English (e.g. 'bibbe' or similar forms) to mean a small cloth fastened about the neck; these forms evolved into the modern English word 'bib'.

Initially the root meant 'to drink' (verb sense). Over time the word developed a common noun sense meaning 'a small cloth to protect clothing', and the verb sense became rare or archaic while the noun sense became the dominant modern meaning.