When Bundgaard arrived in Copenhagen, he undertook a variety of odd jobs until his artistic talents were discovered by Emil Blichfeldt who encouraged him to attend the Technical School in 1884 and later the Danish Academy. It was there that he was introduced to French Naturalism by Stephan Sinding, giving his works with a rather dramatic touch. A stay in Paris also provided him with inspiration from Jules Dalou, Alexandre Falguière and Auguste Rodin. In addition, his father's interest in mythology and folk tales reinforced his imaginative approach which can be seen in his robust, Naturalistic works, often made of granite. His interest in ecclesiastical art from the Middle Ages is also apparent. Bundgaard undertook several major decorative projects including sculptures for the recently built Copenhagen City Hall (1894–99) and for Christiansborg Palace (1907–28) where his four majestic figures stand over the entrance to the parliamentary chamber. Bundgaard's works often exhibit a mythological, nationalistic slant as can be seen in two of his masterpieces, the Gefion Fountain (1908) on Copenhagen's waterfront and the Cimber Bull (1937) in Aalborg. He also completed a number of monuments in commemoration of the volunteers from 1848 and 1864 as well as the Reunification Monument in Randers. Many of Bundgaard's original plaster models can be seen in the Thingbæk Kalkminer Museum, a former mine near the Rebild National Park.
- Gefion Fountain, Copenhagen (1908)
- Statue of Enrico Dalgas, Viborg (1916)
- Decorative work at Christiansborg Palace, Copenhagen (1928)
- Granskende pige, Copenhagen (bronze, 1934)
- Cimber Bull, Aalborg (1937)
- Og dagen rinder med de tusinde krav, Frederiksberg (1938)