Burns provided a copy for The Scots Musical Museum (V, no. 440, p 452) but he didn't write it. Various past discussions here, as both Tibby and Tibbie. "Bee" is an error of transcription, not a traditional variant.

The Susanna Blamire lyric is not the one being asked about, though it was likely written to the same tune, perhaps as an "answer" to the original song.