Born in Chicago, Illinois, Bue received a Bachelor of Philosophy degree from Northwestern University in 1951 and a Bachelor of Laws from the University of Texas School of Law in 1954.

He served as a captain in the United States Army Adjutant General's Department, during World War II, from 1942 to 1946.

He was in private practice at Royston Rayzor in Houston, Texas, from 1954 to 1970.

[1] On August 11, 1970, Bue was nominated by President Richard Nixon to a seat on the United States District Court for the Southern District of Texas vacated by Judge Joe McDonald Ingraham.

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