She was born in London into a theatrical family, the daughter of actors Leigh Murray and his wife Sarah Mannering.
In 1884 at the Comedy Theatre, London, she played in The New Woman, with Fred Terry and Cyril Maude, in 1885 A Leader of Men with Marion Terry and H.B.Irving, and in 1890 A Modern Marriage, opposite Ellaline Terriss and Lewis Waller.
Alma Murray married[2] the poet Alfred William Forman (1840-1925), the first translator of Wagner's Der Ring des Nibelungen.
[1] She played Mrs. Maylie in Oliver Twist (1905), (1912), the Queen in Pelleas and Melisande (1911), Lady Dedmond in Galsworthy's Fugitive (1913), and Mrs. Eynsford-Hill in Shaw's Pygmalion (1914).
A collection of letters between Murray and George Bernard Shaw was privately published in Edinburgh in 1927.