Reliable IMU-only trajectory estimation is crucial for drones operating in GPS-denied or visually degraded environments, where accurate navigation directly impacts safety and mission success. However, achieving accurate and robust drone trajectory estimation using only onboard inertial sensors remains challenging, primarily due to non-stationary measurement noise and time-varying bias drift in low-cost inertial measurement units (IMUs). Motivated by these challenges, this paper presents BDTra, a novel bias-aware, denoising inertial odometry framework that unifies deep learning with model-based sensor fusion to jointly suppress noise, track bias dynamics, and improve long- horizon trajectory consistency. Specifically, BDTra couples three synergistic modules: (i) a deep temporal denoiser that operates directly on raw IMU streams to attenuate high-frequency disturbances while preserving motion cues, (ii) an EKF-based bias filtering model that performs online, dynamic bias estimation and compensation, and (iii) a learning-based, reliability-aware fusion module that adaptively combines denoised and bias-compensated motion hypotheses based on their estimated confidence. The proposed BDTra explicitly models the spectral distortion and phase shifts introduced by neural denoising and mitigates their amplification during inertial integration, thereby retaining short-term maneuver fidelity while reducing long-term drift. Extensive evaluations on two public datasets show that BDTra consistently improves trajectory accuracy over representative inertial odometry baselines. These results indicate that learning-informed bias and noise compensation can substantially enhance IMU-only state estimation for unmanned aerial vehicles.