You're probably using the wrong dictionary

"Fustian", the exemplar word of this polemic, is also a rough fabric, typically worn by servants and ultimately politicised as such, the fabric of the working classes much as the British 1970s socialist worker party obsession with donkey jackets. Worn with pride to show class consciousness.

Before that it was just hardy cotton cloth, used for padding furniture so the Shakespearean sense of "bombast", which is also a fabric, used for padding...

(Bast is a quality of fibre used for spinning.. even bombast is surprisingly technical as a word)