Is the word Бывай! still used in contemporary Russian as a way of saying 'goodbye'?
4 Answers
Yes, this word is in use. But it is rather informal form of "goodbye", for example between good friends
It's one of those semi-obsolete expressions whose usage is either facetious or a personal mannerism.
Also you can use давай
. This word means handshake.
Давай, увидимся! = Goodbye, see you.
Бывай, до встречи! = same as above
Though it has a slightly retro style I guess, it can be used still in inofficial speech like among good friends and such. Derives from wishing good health when saying goodbye ( i.e. бывай здоров)