Daniel D'Addario Chief TV CriticBefore her notoriety as one of Bravo’s “Real Housewives of New York City,” Bethenny Frankel emerged from a very different style of reality TV. In 2005, she competed on “The Apprentice: Martha Stewart,” a show designed to burnish Stewart’s image just after her release from federal prison, and, after having done that, to choose for Stewart a successor figure.