With the increasing importance of data privacy, Local Differential Privacy (LDP) has recently become a strong measure of privacy for protecting each user's privacy from data analysts without relying on a trusted third party. In this paper, we consider the problem of high-utility differentially private release. Given a domain of items and a distance-defined utility function, our goal is to design a differentially private mechanism that releases an item with the global expected error as small as possible. The most common LDP mechanism for this task is the Generalized Randomized Response (GRR) mechanism that treats all candidate items equally except for the true item. In this paper, we introduce Bipartite Randomized Response mechanism (BRR), which adaptively divides all candidate items into two parts by utility rankings. In the local search phase, we confirm how many high-utility candidates to be assigned with high release probability, which gives the locally optimal bipartite classification of all candidates. For preserving LDP, the global search phase uniformly selects the smallest number of dynamic high-utility candidates obtained locally. In particular, we give explicit formulas on the uniform number of dynamic high-utility candidates. The global expected error of our BRR can theoretically deliver a decrease with an asymptotically exact ratio, and when the privacy budget is set to $3$ the expected error can be reduced by $66.4\%$. Extensive experiments demonstrate that BRR outperforms the state-of-the-art methods across the standard metrics and datasets.