Begley was born on January 5, 1915, in Hyden, Kentucky, as the daughter of Felix C. and Ona (Maggard) Feltner.

[2] After graduating from Eastern Kentucky University, Begley worked as a home economics teacher for 30 years.

[2] Following the death of her husband, Elmer, on September 18, 1970, Governor Louie Nunn appointed her to be secretary of state, a position she would hold until her resignation on February 2, 1971.

[1][2] Begley moved from her residence in Hyden, Kentucky to Austin, Indiana in 1975.

She died on May 9, 2010, at Scott Memorial Hospital in Scottsburg, Indiana, at the age of 95.