Spatial transcriptomics are a collection of technologies that have enabled characterization of gene expression profiles and spatial information in tissue samples. Existing methods for clustering spatial transcriptomics data have primarily focused on data transformation techniques to represent the data suitably for subsequent clustering analysis, often using an existing clustering algorithm. These methods have limitations in handling complex data characteristics with varying densities, sizes, and shapes (in the transformed space on which clustering is performed), and they have high computational complexity, resulting in unsatisfactory clustering outcomes and slow execution time even with GPUs. Rather than focusing on data transformation techniques, we propose a new clustering algorithm called kernel-bounded clustering (KBC). It has two unique features: (1) It is the first clustering algorithm that employs a distributional kernel to recruit members of a cluster, enabling clusters of varying densities, sizes, and shapes to be discovered, and (2) it is a linear-time clustering algorithm that significantly enhances the speed of clustering analysis, enabling researchers to effectively handle large-scale spatial transcriptomics data sets. We show that (1) KBC works well with a simple data transformation technique called the Weisfeiler-Lehman scheme, and (2) a combination of KBC and the Weisfeiler-Lehman scheme produces good clustering outcomes, and it is faster and easier-to-use than many methods that employ existing clustering algorithms and data transformation techniques.