Bailey attended Rotherham Grammar School and The Leys School in Cambridge and then studied for a period at Sheffield University.  Bailey was a civil servant in the War Office when he designed his bridge. Another engineer, A.M. Hamilton, successfully demonstrated that the Bailey bridge breached a patent on the Callender-Hamilton bridge, though the Bailey bridge was generally regarded as being superior for temporary use.

Bailey was knighted in 1946 for his bridge design. By this time he was living quietly in Southbourne in Bournemouth. Dorothy Barnes, one of the girls at the Southbourne Crossroads bank, which he used regularly was surprised to learn that her unassuming customer had been knighted. Sir Donald died in Bournemouth in 1985. His 1940s home was demolished c 2004 and replaced by flats, however he also had other addresses in Bournemouth, being recorded in 1974 at 14 Viking Close, as Bailey, Sir Donald C. OBE, JP. The house in which Bailey was born, 24 Albany Street, Rotherham is still standing.

During the Second World War, there was a factory making the components for the Bailey Bridge in the neighbouring town of Christchurch, where a section of bridge still remains, at a retail park in Barrack Road. The components were shipped to training grounds in Cumbria, where men learned the difficult technique of assembling them in rivers at night, to simulate combat conditions. There is, as yet, no blue plaque in Bournemouth to commemorate Sir Donald.