Bleichsteiner was born in Mariahilf and attended the local grammar school from 1901 to 1909.
He went on to study history, geography, ethnography and Oriental languages at the University of Vienna.
He was awarded his doctorate in 1914 and became librarian of the Research Institute for East and Orient, becoming a full member in 1917.
From 1921 he started worked as a volunteer in the ethnographic department of the Natural History Museum, now the Museum of Ethnology, Vienna, being appointed scientific officer in 1926 supervising the Asia Unit.
As an ethnologist Bleichsteiner developed a scientific approach to Central Asia, Siberia and the Caucasus including the languages of these regions.