Powered by multimodal text-to-image priors, diffusion-based super-resolution excels at synthesizing intricate details; however, models trained on synthetic low-resolution (LR) and high-resolution (HR) image pairs often degrade when applied to real-world LR images due to significant distribution shifts. We propose Bird-SR, a bidirectional reward-guided diffusion framework that formulates super-resolution as trajectory-level preference optimization via reward feedback learning (ReFL), jointly leveraging synthetic LR-HR pairs and real-world LR images. For structural fidelity easily affected in ReFL, the model is directly optimized on synthetic pairs at early diffusion steps, which also facilitates structure preservation for real-world inputs under smaller distribution gap in structure levels. For perceptual enhancement, quality-guided rewards are applied to both synthetic and real LR images at the later trajectory phase. To mitigate reward hacking, the rewards for synthetic results are formulated in a relative advantage space bounded by their ground-truth counterparts, while real-world optimization is regularized via a semantic alignment constraint. Furthermore, to balance structural and perceptual learning, we introduce a dynamic fidelity-perception weighting strategy that emphasizes structure preservation at early stages and progressively shifts focus toward perceptual optimization at later diffusion steps. Extensive experiments on real-world SR benchmarks demonstrate that Bird-SR consistently outperforms state-of-the-art methods in perceptual quality while preserving structural consistency, validating its effectiveness for real-world super-resolution. Our code can be obtained at https://github.com/fanzh03/Bird-SR.