Prince Charles Edward Stuart had one [illegitimate] child who survived infancy: Charlotte Stuart, styled Duchess of Albany. Charlotte had two daughters, Marie Victoire Adelaide and Charlotte Maximilienne Amélie, and one son, Charles Edward. For many years the idea was that all three died childless, but in 2002 a man named Peter Pininski published a book documenting his claim that Charlotte's elder daughter, Marie Victoire, did have children, with Jules-Hercule, Prince de Guéméné and Duke of Montbazon.
Peter Pininski went on to document a link to their granddaughter, Julia-Thérèse -- his own great-great-grandmother.
Now, whether or not you accept this theory is up to you. But if it's true, then I suppose Peter Pininski is the closest living descendant of Bonnie Prince Charlie.