In north east Romania, I rarely hear bun venit. It's almost always "bine ați venit!".
You can think of it as "good coming", but the usage is idiomatic. Nowhere else is "venit" used as a standalone word to mean "coming" (that is "venire"). In the idiomatic expression "nou-venit" (newcomer), it means "comer" and, by itself, it means "income".
And what does "venire" look like in my native tongue? "Venir". Gotta love the Romance language family. :)
No, that would be "poftiti." I'm not a native speaker, but I lived in Romania for 2 years and got offered a lot of food, so I'm pretty sure.