I have a Drury Mashburn in my records who MAY be connected to your Drury.
Drury Mashburn was born in July 1850 in Monroe Co., TN. He was the son of David Mashburn (1801 NC) and wife Sarah Brown (1802 TN). Here are the children of David & Sarah, in probably birth order: Matilda, Eliza Louisa, Mary Ann, John Gordon, Lucinda 'Cindy', Lenora, Elizabeth, William Harding, and Drury.
David was the son Of William Mashburn (1780 NC) and wife Mary Jane (1780). Sarah Brown was the daughter of John Gordon Brown (1769 SC) and wife Mary Ann Keicher (1781 NC).
These families, along with their marriages, death dates, and burials are on Ancestry.com.
Keep looking, there is some ancestor named Drury, either given or surname...Good luck