A new and unique plant cultivar of perennial carnation or pinks, Dianthus plant named ‘Double Bubble’ with numerous, small, fully-double, lightly-fragrant flowers producing a rounded full face. Medium pink petals with lighter pink toward apex are irregularly and finely toothed on the distal margin. Heavily branched stems cover the top of the plant with flowers for about six weeks. The habit is compact with long, thin, blue-green foliage.