Bermingham won ten Irish national discus titles: IAAA titles in 1919 and 1920, and NACAI titles in 1923–4–5–6–7, 1930, 1932, and 1933. He held the Irish record at until 1939. He won five English AAA discus titles: 1924–5–6, 1932, and 1934. He also won four Irish titles in each of the 56 lbs weight throw events: for height (1923, 1925–6, 1929) and for distance (1923, 1925–6–7). He represented Ireland at the 1924 Summer Olympics, but was eliminated in the qualifying round of the discus competition; his longest throw would have qualified for the final six but was discounted as a foul. His best mark of ranked him eleventh overall. He is recorded as having competed in the 1934 British Empire Games, though sources vary as to whether he represented the Irish Free State or Northern Ireland. He finished outside the top seven.