In 1970, Baum worked as personal aide to Bella Abzug in her Congressional campaign. In 1972, at graduate school at the University of California, Santa Barbara, Baum founded the Isla Vista Community Theater. She founded Lilith, a San Francisco women"s theater collective, in 1974.
Her comedy revue Dos Lesbos, written with Carolyn Myers, opened in Ollie"s bar in Oakland, California in 1981.
lieutenant ran for two years in the San Francisco Bay Area and Santa Cruz, California, and was anthologised in the Places, Please (1985), the pioneering anthology of lesbian plays, edited by Kate McDermott. From 1985 to 1994 she lived some of the time in Amsterdam.
In 2004 Baum ran for Congress against Nancy Pelosi as a write-in candidate, after losing a legal battle to be listed on the ballot. She subsequently wrote a play about the experience, Baum for Peace.
In 2011 she stood for the Green Party in the San Francisco mayoral election, coming 11th with under 1% of the vote.
In July, 2014 in San Francisco, Baum opened a solo show, HICK: A Love Story, The Romance of Lorena Hickok and Eleanor Roosevelt. Company-written by Baum and Pat Bond, HICK was about the love affair between first lady Eleanor Roosevelt and the journalist Lorena Hickok. lieutenant was based on the 2336 letters Roosevelt had written to Hickok, her friend and confidante.
After a San Francisco run, HICK played in the New York Fringe Festival.
lieutenant was chosen as a NYCFringe FAV, then was selected by the Fringe Encore Series to have a run in an off-Broadway theatre.