It is nearly always one word nowadays : Goodbye. As Michael says, I can't recall ever having seen 'Good-bye' in a long while. You might find it in novels written a long time ago, but the hyphen ( - ) has disappeared from modern usage. I would always use 'Goodbye', if I were you.

there is a common progression of words from two separate words, to hyphenated, to hyphenated or joined, to compound. Witness the 'any' words. 'any thing' probably progressed from 'any thing' -> 'any-thing' -> 'anything' I wouldn't worry too much about whether the hyphen is in or out! Unless the two words are different parts of speech as in 'every day' and 'everyday' that is. Sometimes a hyphen can serve as a hint, or an aid to the eye and brain of the reader (as in 'co-opt') but then, that's another matter altogether...

I can't remember the last time I saw "good-bye". In my opinion, it would be rare now and Oxford doesn't list it as an option. I think it is one of those words which has lost its hyphen over time.

I just looked it up in the dictionary, and both are acceptable.

yes it is the same thin