A copy was made of the manuscript prior to 1450 with "Salthows" signed at the end. It then largely disappeared from public view. Excerpts appeared in 1501 in pamphlets published by Wynkyn de Worde, a prominent London publisher, and again in 1521 by Henry Pepwell, who printed English mystical treatises.
The manuscript turned up in a private library in 1934 and is now in the possession of the British Library. The name at the end was identified as (likely being) Richard Salthouse, a monk at the Norwich cathedral priory. There are notes in different handwriting, and the first page includes Liber Montis Gracie ("Book of Mountegrace"), so it seems that the manuscript passed through the Carthusian priory of Mount Grace in Yorkshire.
The book is interesting as the first medieval autobiography written in English. Some have questioned whether Margery was using this as an attempt at self-aggrandizement, but she refers to herself in the third person, which suggests an attempt at humility rather than celebrity. Unlike other accounts written by mystics, this book is not by a nun or monk or otherwise typical religious member of society. It is a glimpse into a middle-class woman's perceptions of the world and of religious mysticism.
You can read it, digitized, in the original Medieval English, here.
But now for something completely different: appended to the end of the manuscript (not found in the above digitized link) is a recipe. It seems to be a recipe for a sweet medicine. Tomorrow I'll tell you about it, and dragges.