Bogle was born in Chariton, Iowa in 1883. His father, Theodore M. Stuart, Sr., was an Ohio native who established a law practice at Chariton. His mother, Sara (Walker) Stuart was also an Ohio native. Stuart had five siblings: Katie, C.W. Stuart, Col. George W. Stuart, Mrs. Louis Israel, and E. G. Stuart. Stuart attended primary school in the public schools at Chariton. He moved to Denver, Colorado, where his uncle, Thomas B. Stuart, was a judge. Stuart attended high school in Denver, Colorado, and subsequently attended the University of Denver, "pursuing a scientific course." He received a Bachelor of Arts degree from the University of Denver in 1904.