Bissen was trained in the Neoclassical tradition from Bertel Thorvaldsen but after a stay in Paris around 1880, he was influenced by Naturalism.

These included most notably the equestrian statue of King Frederik VII for the plaza in front of Christiansborg Palace (1873).

His notable works include N. F. S. Grundtvig at the Frederik's Church, Christian IV at Nyboder and Queen Consort Caroline Amalie in Rosenborg Castle Garden.

He also produced a large number of animal sculptures of which the birds on the Stork Fountain (1894) on Amagertorv are the most famous.

He held the positions of professor of sculpture at the Royal Danish Academy of Fine Arts 1889-1908.