A new and distinct cultivar of Azalea plant named 'Bittersweet', characterized by its dark green-colored leaves that do not abscise during the cooling and forcing periods; uniform and outwardly spreading plant habit; freely branching habit; uniform and freely flowering habit; rapid flowering response; showy salmon orange-colored flowers; semi-double hose-in-hose flower form with numerous petals and petaloids; excellent postproduction longevity with plants maintaining good flower substance for about five to six weeks in an interior environment; and very good resistance to Cylindrocladium in inoculated trials.