What the difference between saying さようならだ and さようなら? If it had to guess I would be what seems to be obvious, one is declaring it to be goodbye-but is this the case? I've never heard さようならだ used before.
You guessed correctly. However, we say さよならだ much more often than さようならだ. The latter sounds pretty dull. (Vowel lengths are of utmost importance to us.)
With だ, the speaker is declaring a parting. The speaker would be male almost 100% of the time.