Goldsby attended nursing school at Wayne State University in Detroit and worked as a nurse for a while before becoming involved in Urban Ministry in Birmingham. She has worked as a lobbyist on behalf of the City of Birmingham and the Alabama Education Association and has been active in the Jefferson County Citizens Coalition and the Progressive Democratic Council.
She was elected as a delegate to the 1992 and 2000 Democratic National Conventions. She campaigned unsuccessfully for the Alabama House of Representatives in 1993 and 2006, and for the Alabama Senate in 1998. In 2006 she lost in a runoff to Earl Hilliard Jr for the democratic nomination for Alabama House District 60.
Goldsby lives in Fultondale.