Learn Polish: Dziękuję! — Proszę bardzo. - Thank you!

You are right! Proszę is the most common word for "please", but it literally translates to "I ask" or "I request", and bardzo means "very" or "very much". In Polish, proszę bardzo is a versatile set phrase. Aside from "you're welcome", you will also hear it used to mean "here you go" when handing something to someone, or "go ahead" when letting someone pass through a door.

Why do both dziękuję and proszę end in the letter -ę?

The -ę ending shows that "I" am the one doing the action. It is the standard present-tense verb ending for the first person singular (ja, meaning "I"). Because the -ę ending already tells us who is acting, Polish speakers usually drop the word ja and just say dziękuję (I thank) and proszę (I ask/request).

How should I pronounce the -ę at the very end of these words?

The letter ę is a nasal vowel, but when it appears at the very end of a word, it is completely acceptable (and very common) to pronounce it just like a regular, non-nasal "e" (like in the English word "ten"). In everyday, relaxed speech, most Polish speakers say "dziękuje" and "prosze" without the nasal twang at the end.

Do I always have to add bardzo, or can I just say proszę to reply to "thank you"?