[1] He attended the Art School of Toronto with his brother Frederick and in around 1880, Ulric Dunbar emigrated from Canada to the United States to pursue a career in sculpting.

In 1886, he was commissioned to sculpt a model of Vice President Thomas Hendricks that took some four years to complete and was praised for its "straightforward, sober likeness with a degree of honest naturalism".

[3] In his lifetime, Dunbar also sculpted models of Sitting Bull, William Wilson Corcoran, and Frederick Douglass, among many others; more than 150 sculptures are attributed to him.

[3] A copy of Dunbar's bust of Thomas Hendricks, formerly in the collection of the Corcoran Gallery of Art, was upon that institution's dissolution transferred to the American University Museum.

[6] He sculpted a bust of the German-American landscape painter Max Weyl, who also lived in Washington, D.C. and whose works hung in the White House and is in the permanent collection at The Corcoran Art Gallery.