Doswedanja
Formal - До свидания! [d? svi'd?nij?] (doh svi-'da-nja) using only in a personal meetings.
Formal - Всего доброго! [vse'v? 'd?br?v?] (vse-'vo 'dobrovo) mean word-to-word: wishes all of good, often can be previous "До свидания!".
Unformal - Пока [p?-'k?] (po-'ka) - is more nearly to english "bye".
There is unformal - Давай [d?'v??] (da-vai) that more often using between familiar men, familiar youth.
Formal До завтра [d? 'z?vtr?] (do 'zavt-ra) mean "till tomorrow", usually using when you are sure, that will see him (or her) tomorrow, often using unformal.
If you see off someone, can to use "до скорой встречи" [d? 'sk?:r?i 'vstrech?] (do skoroi vstrechi), even if your meeting can be not so soon.
Прощай(те) [pr?'?t???(te)] (proshchai(te)) mean word-to-word "forgive (me)" and using if you will never seen. Use with additional in parentheses for formal farewell or to more old people, or if you want to express very respectful.
It is all that i can to remember just for instance. Of course, there are more versions.
They don't have a word for it, because they never leave.
