He obtained a doctorate in botany at the University of Ghent in 1908. He was an entomologist, and from 1910 to 1912 he was part of la commission Belge sur la maladie du sommeil (Belgian Committee on sleeping sickness). From 1913 to 1915 he worked as a botanist in the Belgian Congo and also collected mollusks.
In 1916 he emigrated to the United States and was an associate researcher from 1917 to 1922 in the American Museum of Natural History.
He became an American citizen in 1921, and taught Entomology at the Harvard Medical School. From 1929 to 1956 he was Curator of insects at the Museum of Comparative Zoology at Harvard, and was Professor of Zoology from 1951 to 1956 within the same institution.
Bequaert became president of the American Malacological Union in 1954. He left his post at Harvard in 1956.
From 1956 to 1960, he lectured in biology at the University of Houston.
With Walter Bernard Miller (1918–2000), he published The Mollusks of the Arid Southwest in 1973.