Baillie is Canadian, and is the daughter of Winnipeg surgeon Alan Klass, and Helen Klass (née Jacob). She has a BA in English from the University of Manitoba and an MA from Oxford.
Before marrying Christopher, Klass was J.R.R. Tolkien's secretary. For the second edition of The Lord of the Rings (Ballantine Books, 1965) she compiled an index to Songs and Verses in the book, complementing the existing index of names.
She edited J.R.R. Tolkien's The Father Christmas Letters for posthumous publication.