Machine learning interatomic force fields are promising for combining high computational efficiency and accuracy in modeling quantum interactions and simulating atomic level processes. Active learning methods have been recently developed to train force fields efficiently and automatically. Among them, Bayesian active learning utilizes principled uncertainty quantification to make data acquisition decisions. In this work, we present an efficient Bayesian active learning workflow, where the force field is constructed from a sparse Gaussian process regression model based on atomic cluster expansion descriptors. To circumvent the high computational cost of the sparse Gaussian process uncertainty calculation, we formulate a high-performance approximate mapping of the uncertainty and demonstrate a speedup of several orders of magnitude. As an application, we train a model for silicon carbide (SiC), a wide-gap semiconductor with complex polymorphic structure and diverse technological applications in power electronics, nuclear physics and astronomy. We show that the high pressure phase transformation is accurately captured by the autonomous active learning workflow. The trained force field shows excellent agreement with both \textit{ab initio} calculations and experimental measurements, and outperforms existing empirical models on vibrational and thermal properties. The active learning workflow readily generalizes to a wide range of systems and accelerates computational understanding and design.