"You are welcome, goodbye!"

Translation: Szívesen, viszlát!

[elipacle]

Why doesnt "Te vagy szívesen, szia" work?

[MartosBogi]

You are welcome is an expression meaning "Szívesen" or "Nincs mit". You do not translate it word by word.
Goodbye is "Viszontlátásra" (formal) or "Viszlát" (informal.
Bye would be "Szia" (Informal between close friends or relatives)

[mizinamo]

szívesen is literally something like "from the heart".

It is not a literal translation of "welcome" -- but Hungarians use szívesen in a context (such as replying to thanks) where some English speakers might use "you're welcome" or "don't mention it" or "it's a pleasure". But it's not a literal translation for any of those.

Treat it as a phrase of its own, equivalent to "you're welcome" or whatever you say, not as an adjective that means "welcome".