The present research investigated the construct validity and psychometric properties of the Self-Compassion Scale (SCS) with a new and advanced statistical procedure, exploratory structural equation modeling (ESEM), in order to contribute to the ongoing discussion about its dimensionality by employing a bifactor-ESEM framework. A Hungarian online representative sample (N = 505, N female = 265, M age = 44.37) filled out the Hungarian version of the SCS. Confirmatory factor analysis (CFA) and ESEM methods were employed, and first-order and bifactor solutions were examined and compared. The bifactor ESEM model demonstrated the best fit to the data with the joint presence of the general self-compassion factor and the specific factors. Internal consistency was adequate in all cases. Reliability indices—omega and omega hierarchical—showed that not all specific factors had unique contributions over and above the general factor. High levels of gender invariance were also achieved with females having lower general self-compassion and self-judgment latent means, while having higher self-kindness scores. The findings shed new light on the underlying theory behind the SCS and proved the usefulness of the bifactor ESEM framework in the investigation of multidimensional constructs.