Found the book with the reference in. It's 'Scottish Songs and Ballads' by Nancy Marshall, 1990.

'This well known and very beautiful old song was originally written by a Lieutenant Hinches as a farewell to his sweetheart. We have no other information about the composer, but we do know that Burns reshaped and improved the original. Burns was also influenced by a song he found in an old anthology written in 1770, with the rather long-winded title 'The Loyal Lover's Farewell to his Sweetheart on going on a |Long Journey.''

This last title I haven't a record of but I'm sure I've seen an earlier song that refers to a red red rose growing on a castle wall that is similar to Burns's first verse.

Stenhouse has little to say on the text other than he had Burns's original ms in front of him, as sent to Johnson, when writing his notes. He mainly writes about the tunes used, 'Major Graham' and 'Mary Queen of Scots lament'.