To be bombastic is to be full of hot air — like a politician who makes grand promises and doesn't deliver.
What does cotton padding have to do with the word bombastic? Bombast was cotton padding or stuffing in the 1500s. Bombastic evolved as an adjective to describe something (or someone!) that is overly wordy, pompous, or pretentious, but the adjective is most often used to describe language (speech or writing). Still not seeing the connection to cotton padding? Think of writing or speech that is overly padded and you'll understand how the meaning came about.