It's a real word, but I think it is just a kind of "baby talk." (I call it "baby talk" but I guess it is more correct to call it "child-directed speech.") In this case, it is used in connection with rocking a baby to sleep.
It is an extension of the work "rock," in much the same as one adds some extra syllables to words to express affection to a young child. The "-bye" part does saying goodbye to someone whom (you hope!) is going to sleep. My mom sometimes wish me "beddie-bye," for example. Similarly "hush-a-bye" means "be quiet, stop crying, goodbye, go to sleep."
In the spirit of adding rhyming or alliterative syllables, in a cooing tone of voice, instead of "bedtime," one might say "sleepy-time." Instead of calling a child "Billy" one might call him "My silly Billy" or "my Billykins."