Tarleton Hoffman Bean was born to George Bean and Mary Smith Bean in Bainbridge, Pennsylvania, on 8 October 1846. He attended State Normal School at nearby Millersport, Pennsylvania, graduating in 1866. He received an M.D. degree from Columbian University, now George Washington University, Washington, DC, 1876.
In 1883, he was awarded an M.S. degree from the Indiana University on the basis of his professional accomplishments, although he did not attend classes there. He married Laurette H. van Hook, daughter of John Welsh VanHook, a local Washington businessman, in 1878 in Washington, DC. They had one daughter, Caroline van Hook Bean (born in Washington on 16 November 1879), a noted artist who later married Bernardus Blommers, Jr.
His brother, Barton Appler Bean, also became an ichthyologist and worked under him at the National Museum.