Active learning, an iterative process of selecting the most informative data pointsfor exploration, is crucial for efficient characterization of materials and chemicalsproperty space. Neural networks excel at predicting these properties butlack the uncertainty quantification needed for active learning-driven exploration.Fully Bayesian neural networks, in which weights are treated as probability distributionsinferred via advanced Markov Chain Monte Carlo methods, offer robustuncertainty quantification but at high computational cost. Here, we showthat partially Bayesian neural networks (PBNNs), where only selected layers haveprobabilistic weights while others remain deterministic, can achieve accuracy anduncertainty estimates on active learning tasks comparable to fully Bayesian networksat lower computational cost. Furthermore, by initializing prior distributionswith weights pre-trained on theoretical calculations, we demonstrate that PBNNscan effectively leverage computational predictions to accelerate active learningof experimental data. We validate these approaches on both molecular propertyprediction and materials science tasks, establishing PBNNs as a practical tool foractive learning with limited, complex datasets.