Her uncle is former governor of Alaska, Mike Stepovich[3] whose daughter, Nada, is married to NBA Hall of Fame player John Stockton.
In 1986, she co-founded the theater company Naked Angels, which she named[4][2] and whose president of the board for many years was John F. Kennedy Jr.
The Naked Angels Theater Company produced many of her plays including The Bluebird Special Came Through Here, directed by Rebecca Miller, I'd Rather Be Punch Drunk (which she starred in as well), and BUSTED (with Ashley Judd in her first stage role), which was on a double bill with the original one act of what was to become Lobby Hero by Kenneth Lonergan produced in conjunction with The John Drew Theater in East Hampton, and Chelsea Walls, directed by Tony Award-winning Edwin Sherin.
Chelsea Walls was originally workshopped and performed for a one-night staged reading with Matt Dillon, Rob Morrow, Nancy Travis and many others at The Minetta Lane Theatre, directed by Roxanne Rogers (sister of Sam Shepard).
Burdette also was involved as both an actor and playwright with Malaparte, who produced her play The Great Unwashed, starring Ethan Hawke, Frank Whaley and Robert Sean Leonard.