I've been in the county's history department a few times but never noticed this sculpture before.
It's by Giovanni-Battista Lombardi, an Italian sculptor who lived from 1823 to 1880.
The bust was originally the property of the Dean Richmond family, and the last family to live in the Richmond Mansion, Watts Richmond, sold it to C.C. Bradley Sr., who donated it the history department in 1978.
It's striking because the veil looks so natural from a slight distance, but step closer and you see it's also marble.
The technique was popularized by sculptor Rafaelle Monti (1818-1881).
Based on a Google search, Lombardi seems to have made several copies of this bust. This one is dated 1866. The Metropolitan Museum of Art lists one in its collection from 1869. Earlier versions seem to exist as well.