Audio-visual speech recognition (AVSR) combines audio-visual modalities to improve speech recognition, especially in noisy environments. However, most existing methods deploy the unidirectional enhancement or symmetric fusion manner, which limits their capability to capture heterogeneous and complementary correlations of audio-visual data-especially under asymmetric information conditions. To tackle these gaps, we introduce a new AVSR framework termed AD-AVSR based on bidirectional modality enhancement. Specifically, we first introduce the audio dual-stream encoding strategy to enrich audio representations from multiple perspectives and intentionally establish asymmetry to support subsequent cross-modal interactions. The enhancement process involves two key components, Audio-aware Visual Refinement Module for enhanced visual representations under audio guidance, and Cross-modal Noise Suppression Masking Module which refines audio representations using visual cues, collaboratively leading to the closed-loop and bidirectional information flow. To further enhance correlation robustness, we adopt a threshold-based selection mechanism to filter out irrelevant or weakly correlated audio-visual pairs. Extensive experimental results on the LRS2 and LRS3 datasets indicate that our AD-AVSR consistently surpasses SOTA methods in both performance and noise robustness, highlighting the effectiveness of our model design.