Eburne was born the daughter of John and Mary Riggs,[1] in Bronte-on-the-Lake, Ontario.

The death of Eburne's father in 1901 was a catalyst for her entry into acting as a profession.

"[1] Eburne began her career in stock theater in Buffalo, New York.

[2] Her early theater work was in Ontario[citation needed] and New York City, debuting on Broadway to great acclaim as "Coddles" in the 1914 farce A Pair of Sixes.

"[4] She continued to play mainly humorous domestic roles on stage, appearing in productions such as The Half Moon (1920), Lady Butterfly (1923), Three Cheers (1928) and Many a Slip (1930),[5] before her first significant film role — and first sound film role —[1] in The Bat Whispers (1930), director Roland West's sound remake of his 1926 silent feature The Bat.