CASTLE is a popular privacy preserving publishing algorithm for k-anonymizing data streams. However, the algorithm does not consider the influence of the distribution of a data stream for clustering, and besides, it has a higher information loss when re-clustering and publishing all the tuples simultaneously. Therefore, in this paper, we propose a novel algorithm of B-CASTLE to solve these deficiencies. B-CASTLE adjusts the tuples into clusters dynamically when clustering, and merges only part of the relevant clusters at a time when publishing. Experiments show that B-CASTLE has a better performance than CASTLE on privacy preservation and efficiency.