Oxford University Press appear to be about to publish the COMPLETE works of Burns. Vols II & III covering Scots Musical Museum due in August 2017.

https://global.oup.com/academic/product/the-oxford-edition-of-the-works-of-robert-burns-9780199683895?cc=gb&lang=en

£250 or $390 (gulp!)

Allowing for the cost of a few reams of paper, you could download the scanned volumes from the link above, print them off and still save yourself a fortune.

http://digital.nls.uk/special-collections-of-printed-music/pageturner.cfm?id=91519813

I searched Bookfinder.com using both "scots musical museum" and "burns musical museum" and it appears that several of the recent "on-demand" publishers have included "in six volumes" in their title despite only offering one volume. Buyer beware.

https://www.bookfinder.com/?ref=bf_s3_hd_2

Ross