Named Entity Recognition (NER) for Bengali medical texts faces significant challenges due to domain-specific terminology, irregular structures, frequent nested entities, and a severe scarcity of annotated resources, leading to critical performance gaps in existing models where high recall is essential to avoid clinical risks. To address this, we propose Bengali Medical Entity Reading Comprehension (BnMERC), a novel framework that formulates NER as a Multi-Question Machine Reading Comprehension (MRC) task. BnMERC integrates a BengaliBERT encoder, a BiLSTM layer for sequential dependencies, an entity-specific query interaction mechanism to resolve overlapping mentions, and a CRF decoder to enable nested and multi-type entity recognition in a single forward pass. We contribute the BMC-NER dataset, a high-quality annotated corpus of Bengali medical conversations and reports featuring nested entities. Rigorous evaluation on BMC-NER, ACE 2005, and GENIA datasets demonstrates that BnMERC outperforms strong baseline models in Micro-F1 and Recall. It excels specifically on nested entities (74.8% F1) and maintains robustness (78.15% F1) on typical Bengali conversation words, where other models degrade. This work provides a new solution for low-resource Bengali clinical NER, advancing domain-specific information extraction.