She was born as Edith Drury on 27 June 1870 in St Pancras workhouse in London, where her Limerick born father, Michael Drury worked as an attendant. Her mother Agnes Hopton was Welsh. Costello, then Miss Drury, became a teacher. She was a member of the various Irish organisations in London and became a member of the Gaelic League when it formed. It was there she learned Irish. A member of the committee, she was a representative on behalf of the London Branch at the Ardfheis in May 1902. Costello began collecting Irish language songs in London (she first collected 'Neillí Bhán' on a train coming from Woolwich). She came to live in Tuam, County Galway, Ireland when she married Dr Thomas Bodkin Costello in 1903. He was a medical doctor, historian, and fellow Gaelic Leaguer. They had a daughter, the writer Nuala Costello'
Costello's collecting work really began in Tuam. Although she supplied extensive source-notes to the songs and information on their backgrounds (with English translations mainly by others), her motivation was not academic. She intended her volume primarily 'for popular use in the schools and Gaelic League classes of Connacht'.
Costello was involved in the Irish War of Independence in Tuam. She was elected to the Irish Free StateSeanad Éireann as an independent member in December 1922. She was one of four women elected or appointed to the first Seanad in 1922. She was re-elected until she lost her seat in the 1934 Seanad election. Of the four women in the Senate, Costello was the only one who spoke to any notable extent. She was one of only two of the women senators who spoke against the The Civil Service Regulation Bill, which would make it legal for the government to confine certain jobs to specific sexes and the Juries Bill which would require women to volunteer for jury service instead of it being a standard part of citizenship.
In 1919, Costello published a compilation of traditional folk-songs from County Galway and County Mayo, titled Amhráin Muighe Seola: Traditional folk-songs from Galway and Mayo.