Translation:Goodbye, Elizabeth and Alasdair.
the way I undertand it, "mar sin leibh" (or "leat", addressing a peer) meaning "as so with you" is the response to someone saying, "slàn leibh" (or "leat") in parting, meaning "a clear way for you" or "safety with you". It can be said after another parting blessing, too, such as "soraidh slàn." As in English, we might say, "safe home" meaning, "I hope you get home safely" and the reply would be, "you too!" the translation to "goodbye" stems from original meanings of farewell, "fare thee well" and goodbye, "God be with ye". Both these English parting wishes are similar encouraging sentiments to these Scottish parting wishes above. Many languages offer a parting blessing, for example, Spanish "adiós" and Turkish "allahaısmarladık."
Sorry to be pedantic, but Goodbye comes from God bless you. It cannot possible come from God bless *ye as ye was nominative only until much later - see usage notes. DaibhidhR
Etymonline begs to differ. good-bye salutation in parting, also goodbye, good bye, good-by, 1590s, from godbwye (1570s), a contraction of God be with ye (late 14c.), influenced by good-day, good evening, etc. As a noun from 1570s. Intermediate forms in 16c. include God be wy you, God b'uy, God buoye, God buy, etc.
Yes, you will always see different things in different sources. The annoying thing about etymologies, not only in public-contribution sites such as Etymonline, but even in reputable sources like the OED and Merriam-Webster, is that they don't give sources to support their etymologies, even if they do give citations as evidence of the use of the word. In this case, Etymonline does provide evidence of the claimed 14th-century expression, which is inherently hard to believe. It also contradicts itself, since the entry for ye in Etymonline in unequivocal in stating that it is nominative only. It is easy for someone not familiar with Early Modern English (which might include the writer of the article on good-bye) not to see the difference as important. I think most people who have studied Shakespeare at school will have appreciated that ye is is a variant of you without actually appreciating that it is only used in certain circumstances.
I searched online for examples of ye 1400-1612 and examples in the accusative were vanishly rare. The Book of Common Prayer, the Bible and Shakespeare had ye occurring only in the nominative and vocative. Other works had it as variant spelling of the and, exceptionally rarely, in the accusative. One of the few I did find was England's Helicon but even here the occurrences were vastly outnumbered by you, being essentially limited to one poem. Indeed I challenge you to find any source from this period that uses ye in the accusative as anything other than a rare variant of you.
I think the author in Etymonline may have been influenced by the orthographic similarity of good-bye and ye. However the pronunciation is very different and Etymonline itself suggests that good-bye is influenced by good-day. I would guess that the slender vowel in God bless you had something to do with it too. DaibhidhR
There seems to be very little evidence (i.e. none quoted here) and a lot of hearsay as to where this comes from.
But, simply by looking the word-for-word meaning ('like that with you') it is pretty obvious that it is a reply, and most likely a reply to something that had leat 'with you' in it. Your suggestion, 'blessing with you', or 'bless you' as we say in English, is the only sensible thing I can think of. It is used in the small Catholic Gaelic-speaking area of Scotland, but never in the predominant Presbyterian area. It is also, of course, used in Ireland by default, since there, unlike in Scotland, their Gaeilge is, at least historically, pretty well restricted to Catholics.
No, it's just more formal. Tioraidh is like Cheerio! and Mar sin leat (or leibh) more like Goodbye. I also hear people on TV, including kiddie cartoon characters, saying "Slan leat" (or leibh) quite a lot, which I believe is said to be even more formal. But that's hard to sustain when you hear a rabbit in a jumpsuit saying it, so I'm not certain.