This paper presents an efficient method to compute space-time superpixels and an application of the superpixels called superpixel convolution. The space-time superpixel method extends a single-image Bayesian method named BASS. Our approach, named Bayesian-inspired Space-Time Superpixels (BIST), is inspired by hill-climbing to a local mode of a Dirichlet-Process Gaussian Mixture Model conditioned on the previous frame's superpixel information. The method is only Bayesian-inspired, rather than actually Bayesian, because the split/merge steps are treated as a classification problem rather than derived from a Gibbs sampling update step. However, this heuristic reduces the number of split/merge steps from several hundred per frame to only a few. BIST is over twice as fast as BASS and over 10 times faster than other space-time superpixel methods with favorable (and sometimes superior) quality. Additionally, to garner interest in superpixels, this paper demonstrates their use within deep neural networks. We present a superpixel-weighted convolution layer for single-image denoising that outperforms standard convolution by 1 dB PSNR.