Although Approximate Nearest Neighbor (ANN) search has been extensively studied, large-k ANN queries that aim to retrieve a large number of nearest neighbors remain underexplored, despite their numerous real-world applications. Existing ANN methods face significant performance degradation for such queries. In this work, we first investigate the reasons for the performance degradation of quantization-based ANN indexes: (1) the inefficiency of existing top-k collectors, which incurs significant overhead in candidate maintenance, and (2) the reduced pruning effectiveness of quantization methods, which leads to a costly re-ranking process. To address this, we propose a novel bucket-based result collector (BBC) to enhance the efficiency of existing quantization-based ANN indexes for large-k ANN queries. BBC introduces two key components: (1) a bucket-based result buffer that organizes candidates into buckets by their distances to the query. This design reduces ranking costs and improves cache efficiency, enabling high performance maintenance of a candidate superset and a lightweight final selection of top-k results. (2) two re-ranking algorithms tailored for different types of quantization methods, which accelerate their re-ranking process by reducing either the number of candidate objects to be re-ranked or cache misses. Extensive experiments on real-world datasets demonstrate that BBC accelerates existing quantization-based ANN methods by up to 3.8x at recall@k = 0.95 for large-k ANN queries.