In this paper, we propose an efficient continuous-time LiDAR-Inertial-Camera Odometry, utilizing non-uniform B-splines to tightly couple measurements from the LiDAR, IMU, and camera. In contrast to uniform B-spline-based continuous-time methods, our non-uniform B-spline approach offers significant advantages in terms of achieving real-time efficiency and high accuracy. This is accomplished by dynamically and adaptively placing control points, taking into account the varying dynamics of the motion. To enable efficient fusion of heterogeneous LiDAR-Inertial-Camera data within a short sliding-window optimization, we assign depth to visual pixels using corresponding map points from a global LiDAR map, and formulate frame-to-map reprojection factors for the associated pixels in the current image frame. This way circumvents the necessity for depth optimization of visual pixels, which typically entails a lengthy sliding window with numerous control points for continuous-time trajectory estimation. We conduct dedicated experiments on real-world datasets to demonstrate the advantage and efficacy of adopting non-uniform continuous-time trajectory representation. Our LiDAR-Inertial-Camera odometry system is also extensively evaluated on both challenging scenarios with sensor degenerations and large-scale scenarios, and has shown comparable or higher accuracy than the state-of-the-art methods. The codebase of this paper will also be open-sourced at https://github.com/APRIL-ZJU/Coco-LIC.