Pompous language is imagined as verbal stuffing.
Earlier bombace named raw cotton. Bombast was used for padding or stuffing, then figuratively for language inflated with pretension.
The sources differ on the deeper relationship between cotton and silk words. This trail stays with the documented English material, padding and rhetorical uses.
Source
Merriam-Webster: bombastThe entry records earlier textile padding and bombace, and distinguishes the deeper cotton and silk histories.