We present a theoretical framework for the thermodynamic properties of supercoiling-induced denaturation bubbles in circular double-stranded DNA molecules. We explore how DNA supercoiling, ambient salt concentration, and sequence heterogeneity impact on the bubble occurrence. An analytical derivation of the probability distribution to find multiple bubbles is derived and the relevance for supercoiled DNA discussed. We show that in vivo sustained DNA bubbles are likely to occur due to partial twist release in regions rich in weaker AT base pairs. Single DNA plasmid imaging experiments clearly demonstrate the existence of bubbles in free solution.