'bayeta' originates from Spanish, specifically the word 'bayeta', meaning 'a kind of soft cloth'.

'bayeta' entered English from Spanish (and through trade contacts) in the modern period; it retained the Spanish form and sense as a term for a soft, thick fabric.

Initially, it meant 'a type of soft cloth' in Spanish, and over time it has kept the same basic meaning in English as 'a soft, thick cloth used for cleaning or upholstery'.