Bajoie received a bachelor's degree in political science from historically blackSouthern University in Baton Rouge. At the age of twenty-seven, she was initially elected in 1975 to the Louisiana House of Representatives from District 91 in her native New Orleans. At the time, the state instituted its unique nonpartisan blanket primary. In her first term, she was the only woman among the 105 House members. Early in 1991, she left the House after becoming the first black female ever elected to the Louisiana State Senate. This was twenty-five years after Barbara Jordan achieved the same distinction in neighboring Texas. Bajoie's Senate service began in District 5 in February 1991, when she won a special election to succeed African-American state Senator-turned-U.S. Representative William J. Jefferson. Bajoie polled 53 percent of the vote over four opponents from both parties in a low-turnout contest. She held the Senate seat until 2008, when she was term-limited by Louisiana law. As a legislator, Bajoie was an advocate for school-based health clinics. She worked to establish the Minority Health Care Commission and sought to expand health care coverage for citizens with mental disorders. She worked to establish the Louisiana State Museum on Civil Rights as well as the expansion and renaming of the New Orleans Convention Center to honor Ernest Morial, who was elected in 1978 as the first black mayor of New Orleans. She was a founder and former chair of the Louisiana Legislative Black Caucus and the Louisiana Legislative Women’s Caucus. She is a former president of the National Organization of Black Elected Legislative Women. She advises young people to be "civic-minded" and to project the "needs of the community at the center of everything...."
Post-legislative career
Years after she obtained her undergraduate degree, Bajoie studied for a master's degree in health administration. Bajoie ran unsuccessfully for the New Orleans City Council in the primary election held on October 20, 2007. At the time, she could not run for the state Senate. She polled only 11 percent of the vote in District B. Nearly five years later, however, Mayor Mitch Landrieu temporarily appointed her to the seat upon the resignation of fellow Democrat Stacy Head, who was instead named to an at-large council position in an election held in March 2012. As the director of community relations for the LSU Health Sciences Center, Bajoie performs liaison work with the deans of each of the six schools under the center. She focuses upon the promotion of cultural diversity. Bajoie left the city council in 2013. In 2007, Bajoie was inducted into the Louisiana Political Museum and Hall of Fame in Winnfield.