Privacy-preserving data analytics has received much attention in recent years. However, existing local privacy-preserving mechanisms struggle to address data generation bias and distribution shifts, which makes it difficult to achieve the optimal privacy-utility trade-off in downstream data analysis tasks. In this paper, we propose a privacy-preserving K-means clustering framework: Bounded Perturbation Generation Mechanism and TK-means (BPGT), aiming to balance between robust privacy preservation and high data utility. On the one hand, we propose the bounded perturbation generation mechanism, which combines bounded noise sampling with synthetic data generation based on gradient descent. This mechanism mitigates the cumulative error problem inherent in traditional local differential privacy methods while ensuring \(d_{\chi }\) -privacy. On the other hand, we propose the TK-means algorithm integrating the T-Mixture Model and the Expectation Maximization algorithm to enhance the robustness of the K-means algorithm to complex data distributions and outliers. To evaluate the performance of our method, we provide theoretical guarantees on privacy preservation and data utility, and verify its effectiveness through extensive experiments. The results show that BPGT improves on average 9.11% and 7.51% in clustering accuracy and 76.35% in error control compared to existing methods.