In English and Spanish, the words for welcome have an uncanny relation: the translation is almost completely (if not completely) literal.Bien means well and venidos means come/came in the plural or something along those lines. I looked up if it came from Latin (in English welcome), and it said that it didn’t. So, I am wondering if there is a reconstructed PIE phrase of invitation that translated as “(you’re) well, come” or something like that.
The etymology of the two expressions goes back to different sources, but the conceptual link is somewhat similar. "Welcome" goes back to "will" and not to "well" (etymonline.com/word/welcome). So the semantic origin would be something along the lines of "your coming suits my will/wish". "Bienvenidos" and Romance cognates, instead, go back to Latin "bene" ('well'). There is no exhaustive explanation in the etymological dictionaries of Romance languages that I have consulted, but the semantics should be something like "I consider your coming good".