This paper introduces a novel two-stage active learning (AL) pipeline for automatic speech recognition (ASR), combining unsupervised and supervised AL methods. The first stage utilizes unsupervised AL by using x-vectors clustering for diverse sample selection from unlabeled speech data, thus establishing a robust initial dataset for the subsequent supervised AL. The second stage incorporates a supervised AL strategy, with a batch AL method specifically developed for ASR, aimed at selecting diverse and informative batches of samples. Here, sample diversity is also achieved using x-vectors clustering, while the most informative samples are identified using a Bayesian AL method tailored for ASR with an adaptation of Monte Carlo dropout to approximate Bayesian inference. This approach enables precise uncertainty estimation, thereby enhancing ASR model training with significantly reduced data requirements. Our method has shown superior performance compared to competing methods on homogeneous, heterogeneous, and OOD test sets, demonstrating that strategic sample selection and innovative Bayesian modeling can substantially optimize both labeling effort and data utilization in deep learning-based ASR applications.