Syntax-guided synthesis has been a prevalent theme in various computer-aided programming systems. However, the domain of bit-vector synthesis poses several unique challenges that have not yet been sufficiently addressed and resolved. In this paper, we propose a novel synthesis approach that incorporates a distinct enumeration strategy based on various factors. Technically, this approach weighs in subexpression recurrence by term-graph-based enumeration, avoids useless candidates by example-guided filtration, prioritizes valuable components identified by large language models. This approach also incorporates a bottom-up deduction step to enhance the enumeration algorithm by considering subproblems that contribute to the deductive resolution. The implementation of the enhanced enumeration techniques, named Biten, outperforms state-of-the-art solvers in terms of the number of solved problems, execution time, and solution size. Notably, Biten successfully solved 32 synthesis problems for the first time, including 6 renowned Hacker’s Delight problems.