I hear this phrase often from waiters at restaurants when a patron is leaving, but they say it so quickly that I can't recognize what they say; it seems that the last word is "bien" and the whole phrase consists of 2-3 words.
"Que le vaya bien" literally means "Farewell"
in some places people still use
"Vaya con Dios" for the same purpose which is equivalent to "Godspeed"
Its an ubiquitous phrase to use when parting ways with someone you don't really know or are close with, hence the formal mode "Que le vaya bien" instead of the informal "que te vaya bien"
Why would a server bid farewell to his patron? (Something i've rarely seen in the states, but it's an everyday occurrence in mexico.)
Well , It's simply good manners, a show gratitude for the tips received, and plain good business practice.
Tal y como indicó aris en los comentarios, puede tratarse de distintas opciones:
- Que le vaya bien
- Que esté bien
Que le vaya bien -- definitely. It's as ubiquitous as "Enjoy the rest of your day" has become recently in the US -- or more, even. To a tourist or obvious foreigner, it might be Que te vaya bien.