In Chambers Scots Dictionary "busk" is also given as 'get ready' which I find a little more generally satisfying the 'get dressed'.
Robert Ford, in his 'Vagabond Songs and Ballads of Scotland' (1899) wrote of the song,
"Fifty years ago this was a popular song in Perthshire, to which county, by authorship it belongs.
The writer, James Duff, known as 'The Methven Poet,' was a gardener to trade and flourished in the early years of the present century.
A volume of his poems was published at Perth in 1816

Gavin Greig's not in The Greig Duncan collection reads:
LASSIE WI' THE YELLOW COATIE Cf. Ford, p. 198. Alan Reid gives the following note with a version in the Rymour Club Miscellanea, 2.119: "The complete text of this popular old song has a place in Ford's Vagabond Ballads, but without the air, which neither Mr Ford nor I could gather when his book was in preparation. Mrs Jessie Patrick Findlay has, however, been able to recover it, the set here given having been noted from her mother's singing. The popular version, a single stanza of which accompanies the music, was written by James Duff, the Methven poet, and appears in his volume of Poems and Songs, published by Morrison, Perth, in 1816. Another and entirely different version of the song and air, attributed to John Hamilton of 'Cauld and Raw' fame, is given in [James Wood and Learmont Drysdale,] Song Gems [London, 1908, pp. 128-9]." "From the place-name in our version [B] of 'Lassie wi' the Yellow Coatie' people in the north have taken the song to belong to Donside. Ford, however, who does not give the localising verse, says the song belongs to Perthshire, and was written by James Duff, known as 'The Methven Poet,' who was a gardener to trade, and published a volume of his poems [A Collection of Poems, Songs, Etc., chiefly Scottish] at Perth in 1816. Although the song appears in this volume [pp. 172-3] as the production of Duff, it is quite possible that he worked on an older model. Ford himself says that Duff's book contains a somewhat flabby and diffuse version of 'Bessie Bell and Mary Gray,' and that the song, 'Lassie wi' the Yellow Coatie,' is the only one of his productions which has attained any popularity. All which is just a little significant. The tune, which is very pretty, does not seem particularly old in its present form, but we should not wonder if it were an adaptation from a strathspey of the type of 'Whistle o'er the Lave o't.' As it stands, it suggests an affinity with [348] 'Jock o' Rhynie.' A variant will be found in 'Can Ye Lo'e Me Weel, Lassie?' in Lyric Gems (1856)."
Jim Carroll