In the first case, it is set as a rowing song, appearing in a work of fiction. Katherine Foot included it in a story, "Marcia's Fortune," that she wrote for Scribner's, April 1877. Here's the passage.
Just then the sound of a voice singing reached her ears, and she turned her head to see a little boat, with two men in it, row past—as near in shore as was safe. One was a gunner, and the other a man she knew well,—a broken-down sailor who had once shipped “able-bodied seaman,” but whose day for that had long been over. As he rowed he trolled out an old sea-song, sung by many a sailor as he weighed anchor or reefed top-sails, outward bound. It was this:
“I'm bound away to leave you;
Good-bye, my love, good-bye!
Don't let my absence grieve you;
Good-bye, my love, good-bye!”
Then in 1882, in his famous article for Harper's, W.L. Alden quoted the song, calling it a pulling song:
I'm bound away to leave you
Good-by, my love, good-by
I never will deceive you
Good-by, my love, good-by...
Davis and Tozer picked this up for their collection—seemingly directly from Alden—and created a bunch of extra verses. It was also passed down to Joanna Colcord and C. Fox Smith. This stream is what appears in the second part of my video, preceded by Hugill's offering.
Goodbye, my love,