Bailey was born in Devizes, Wiltshire, and raised from age 10 onwards on a farm in western Australia without formal education. While growing up, he learned German, Italian, Spanish, Latin, and Greek from household books, and Russian from a neighbor. After he grew interested in the lettering on tea-chests from India, he acquired a book of Bible selections translated into languages with non-European scripts, including Tamil, Arabic, and Japanese. By the time he had left home, he was reading Avestan as well.
In 1921 he entered the University of Western Australia to study classics. In 1927, after completing his master's degree on Euripedes, he won a Hackett Studentship to Oxford where he joined the Delegacy of Non-Collegiate Students, later St Catherine's College. After graduating with first class honours in 1929, he was appointed as Parsee Community Lecturer in the then London School of Oriental Studies. That same year he began his doctoral dissertation, a translation with notes of the Greater Bundahisn, a compendium of Zoroastrian writings in Middle Persian recorded in the Pahlavi script. In 1937 he became Chair of Sanskrit and a Fellow at Queens' College, Cambridge and was succeeded at SOAS by W. B. Henning. He retired in 1967.
Bailey has been described as one of the greatest Orientalists of the twentieth century. He was said to read more than 50 languages, and was the world's leading expert in Khotanese, the mediaeval Iranian language of the kingdom of Khotan in Chinese Turkestan. He was known for his immensely erudite lectures, and once confessed: "I have talked for ten and a half hours on the problem of one word without approaching the further problem of its meaning." After his death, he left his enormous library to the Ancient India and Iran Trust in Cambridge.
Bailey was elected a Fellow of the British Academy in 1944, and subsequently a member of the Danish, Norwegian and Swedish Academies. He received honorary degrees from four universities including Oxford; served as president of Philological Society, the Royal Asiatic Society, the Society for Afghan Studies, and the Society of Mithraic Studies; and chaired the Anglo-Iranian Society and Ancient India and Iran Trust. He was knighted for services to Oriental studies in 1960.