Ulla Barding-Poulsen fenced for the Akademisk Fægteklub in København, Denmark. Barding-Poulsen was part of the Danish team that won the European Championships in 1932 in the foil event. At the World Championships, Barding-Poulsen won a team gold in 1947 and 1948, a silver in 1950, and a bronze in 1937 and 1951. Barding-Poulsen also competed at two Olympic Games. At the 1936 Berlin Olympics, she reached the quarter-finals in the individual foil event. At the 1952 Helsinki Olympics, Barding-Poulsen was eliminated in the opening round after only winning two of her bouts in her pool.