Autonomous bicycles offer a promising agile solution for urban mobility and last-mile logistics. However, conventional control strategies often struggle with underactuated nonlinear dynamics, suffering from sensitivity to model mismatches and limited adaptability to real-world uncertainties. To address this, we develop CycleRL, a comprehensive sim-to-real framework for robust autonomous bicycle control. Our approach establishes a direct perception-to-action mapping within the high-fidelity NVIDIA Isaac Sim environment, leveraging Proximal Policy Optimization (PPO) to optimize the control policy. The framework features a composite reward function tailored for concurrent balance maintenance, velocity tracking, and steering control. Crucially, systematic domain randomization is employed to reduce the reliance on precise system modeling, bridge the simulation-to-reality gap and facilitate direct transfer. In simulation, CycleRL achieves promising performance, including a 99.90% balance success rate, a heading tracking error of 1.15°, and a velocity tracking error of 0.18 m/s. These quantitative results, coupled with successful hardware deployment, validate DRL as an effective paradigm for autonomous bicycle control, offering superior adaptability over traditional methods. Video demonstrations are available at https://anony6f05.github.io/CycleRL/.