A new cultivar of Aster plant named ‘Billowing Pink’ that is characterized by its uniform, rounded and dense mounded plant habit, its clumping forming growth habit, its sticky, aromatic foliage that is not appealing to deer or rabbits, its very good resistance to rust, powdery mildew and lace bug predation, and its inflorescences with ray florets that are wider in size and pink-violet in color with the color persistent for the duration of bloom and strongly upturned at inception and remain somewhat upturned throughout the blooming period.