Large language models (LLMs) frequently exhibit performance biases against regional dialects of low-resource languages. However, frameworks to quantify these disparities remain scarce. We propose a two-phase framework to evaluate dialectal bias in LLM question-answering across nine Bengali dialects. First, we translate and gold-label standard Bengali questions into dialectal variants adopting a retrieval-augmented generation (RAG) pipeline to prepare 4,000 question sets. Since traditional translation quality evaluation metrics fail on unstandardized dialects, we evaluate fidelity using an LLM-as-a-judge, which human correlation confirms outperforms legacy metrics. Second, we benchmark 19 LLMs across these gold-labeled sets, running 68,395 RLAIF evaluations validated through multi-judge agreement and human fallback. Our findings reveal severe performance drops linked to linguistic divergence. For instance, responses to the highly divergent Chittagong dialect score 5.44/10, compared to 7.68/10 for Tangail. Furthermore, increased model scale does not consistently mitigate this bias. We contribute a validated translation quality evaluation method, a rigorous benchmark dataset, and a Critical Bias Sensitivity (CBS) metric for safety-critical applications.