From the Burns on line encyclopedia
http://www.robertburns.org/encyclopedia/UrbaniPietro17491511816.871.shtml


I got this:The song first appeared in Urbani's Scots Songs, 1794, to an original tune. In his publication, Urbani explained that: '... the words of the RED, RED ROSE were obligingly given to him by a celebrated Scots Poet, who was so struck with them when sung by a country girl that he wrote them down, and, not being pleased with the air, begged the Author to set them to Music in the style of a Scots Tune, which he has done accordingly.'

The first three stanzas of the song appeared in the Museum, 1797, to the Gow tune 'Major Graham', the tune Burns himself specified. It also appeared in Thomson's Original Scottish Airs, 1799, 'improved' by the insensitive editor to fit Marshall's 'Wishaw's Favourite', a tune of double measure (i.e. 'And fair thee weel awhile' became 'And fair thee weel a little while'!)

The 'Red, Red Rose', however, only achieved popularity when matched to 'Low down in the Broom', and air which first appeared in the Caledonian Pocket Companion. Burns's words and the air 'Low down in the Broom' were first brought together by the Paisley composer and editor, Robert Archibald Smith, in his Scottish Minstrel, published in 1821.

Does anyone know of a version from before 1790 or have any suggestions about where I might look?
Robbie