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Measuring the relevance between user queries and advertisements is a critical task for advertisement (ad) recommendation systems, such as Microsoft Bing Ads and Google Ads. Traditionally, this requires expert data labeling, which is both costly and time-consuming. Recent advances have explored using Large Language Models (LLMs) for labeling, but these models often lack domain-specific knowledge. In-context learning (ICL), which involves providing a few demonstrations, is a common practice to enhance LLM performance on domain-specific tasks. However, retrieving high-quality demonstrations in a vast exploration space remains challenging. In this paper, we introduce ICL-Bandit, a practical and effective approach that leverages ICL to enhance the query-ad relevance labeling capabilities of LLMs. We develop a novel bandit learning method to identify and provide superior demonstrations for ICL, thereby improving labeling performance. Experimental results demonstrate that ICL-Bandit achieves state-of-the-art performance compared to existing methods. Additionally, ICL-Bandit has been deployed in Company X, that serves billions of users worldwide, confirming its robustness and effectiveness.