While there has been significant progress in ASR, African-accented clinical ASR has been understudied due to a lack of training datasets. Building robust ASR systems in this domain requires large amounts of annotated or labeled data, for a wide variety of linguistically and morphologically rich accents, which are expensive to create. Our study aims to address this problem by reducing annotation expenses through informative uncertainty-based data selection. We show that incorporating epistemic uncertainty into our adaptation rounds outperforms several baseline results, established using state-of-the-art (SOTA) ASR models, while reducing the required amount of labeled data, and hence reducing annotation costs. Our approach also improves out-of-distribution generalization for very low-resource accents, demonstrating the viability of our approach for building generalizable ASR models in the context of accented African clinical ASR, where training datasets are predominantly scarce.