Efficient and accurate product relevance assessment is critical for user experiences and business success. Training a proficient relevance assessment model requires high-quality query-product pairs, often obtained through negative sampling strategies. Unfortunately, current methods introduce pooling bias by mistakenly sampling false negatives, diminishing performance and business impact. To address this, we present Bias-mitigating Hard Negative Sampling (BHNS), a novel negative sampling strategy tailored to identify and adjust for false negatives, building upon our original False Negative Estimation algorithm. Our experiments in the Instacart search setting confirm BHNS as effective for practical e-commerce use. Furthermore, comparative analyses on public dataset showcase its domain-agnostic potential for diverse applications.