Edward B. Bury was born on April 21, 1839, in Washington, D.C., to Eliza Bury. He grew up and attended school in Washington, and by 1860, he was working as an apothecary.
He enlisted in the Union army on April 18, 1861, and he mustered in as a private in Company B of the 4th District of Columbia Militia Infantry Battalion. He mustered out on July 17, 1861.
He remained in Washington after leaving the army, and he earned a living as a druggist. By 1870, he owned $1,000 of personal property. He also worked as a pension attorney. He apparently never married, and he lived with his sisters until at least 1900. He applied for a federal pension in July 1904 and eventually secured one. He died on July 5, 1918.