All that can presently (September 2022) be gleaned about Rose Gower from sheet music covers and by Internet searching is that she was presumably an English music hall performer who has been featured on just one work namely Come and Take Tea With Me (1910) music by Charles Collins, words by Fred J Barnes and published by Francis, Day & Hunter, London W.C.2, England.
Surfers are welcome to contribute any further information about this performer.