A new cultivar of grandiflora rose, Rosa `BAIsme`, characterized by its clusters of double flowers that are a blend of rosy-pink and apricot in color, its upright mounded plant habit, and its abundant flowers present in May and June and recurrently throughout the season over medium green, satiny, foliage that is resistant to rose blackspot and powdery mildew. The new variety is readily propagated on its own roots and hardy in U.S.D.A. Zones 5 to 9.