Unmanned Aerial Vehicles (UAVs) play an important role in various applications, where precise trajectory tracking is crucial. However, conventional control algorithms for trajectory tracking often exhibit limited performance due to the underactuated, nonlinear, and highly coupled dynamics of quadrotor systems. To address these challenges, we propose HBO-PID, a novel control algorithm that integrates the Heteroscedastic Bayesian Optimization (HBO) framework with the classical PID controller to achieve accurate and robust trajectory tracking. By explicitly modeling input-dependent noise variance, the proposed method can better adapt to dynamic and complex environments, and therefore improve the accuracy and robustness of trajectory tracking. To accelerate the convergence of optimization, we adopt a two-stage optimization strategy that allow us to more efficiently find the optimal controller parameters. Through experiments in both simulation and real-world scenarios, we demonstrate that the proposed method significantly outperforms state-of-the-art (SOTA) methods. Compared to SOTA methods, it improves the position accuracy by 24.7% to 42.9%, and the angular accuracy by 40.9% to 78.4%.