Ace was a young earth teenager working as a waitress in the frozen food retail complex of Iceworld on the planet Svartos when she first came across the Doctor and Mel. Almost immediately she impresses the Doctor with her intelligence and enthusiasm. After assisting the Doctor and Mel in their adventure on Svartos, when Mel decides to stay behind, Ace is more than willing to accept the Doctor's offer to get off this planet and go adventuring.
Ace was what would be called a troubled child back on earth, who was expelled from school for blowing up the art room. That along with a bad relationship with her mother and a variety of other traumatic events, leads Dorothy to adapt a tough exterior. While experimenting with some nitroglycerine Dorothy was swept up in a time tunnel and brought to the planet Svartos, many years in the future. She wouldn't learn until much later that her plight was the result of a plot by one of the Doctor's enemies.
Explosives seem to be of particular interest to Ace. Although the Doctor frequently chastises her for using Nitro-9, an explosive concoction of her own design, it often comes in handy in difficult situations. Ace is also all about being prepared. There was hardly a time when she could be seen without her back pack full of all sorts of things. You never know when a baseball bat or a boom box might come in handy.
Under the Doctor's tutelage, Ace grows into a mature young woman. Although the Doctor often appears to be manipulative and mysterious, his actions frequently call for her to collect the facts and make up her own mind. Along the way, he helps her deal with many of the issues of her past.
It's iunclear how the Doctor and Ace parted ways, but Sarah Jane mentions to her kids years later that she tried to track down some of the Doctor's companions. She mentions "that Dorothy something — she runs that charity, 'A Charitable Earth' ("ACE"). She's raised billions."