Noise robustness is critical when applying automatic speech recognition (ASR) in real-world scenarios. One solution involves the used of speech enhancement (SE) models as the front end of ASR. However, neural network-based (NN-based) SE often introduces artifacts into the enhanced signals and harms ASR performance, particularly when SE and ASR are independently trained. Therefore, this study introduces a simple yet effective SE post-processing technique to address the gap between various pre-trained SE and ASR models. A bridge module, which is a lightweight NN, is proposed to evaluate the signal-level information of the speech signal. Subsequently, using the signal-level information, the observation addition technique is applied to effectively reduce the shortcomings of SE. The experimental results demonstrate the success of our method in integrating diverse pre-trained SE and ASR models, considerably boosting the ASR robustness. Crucially, no prior knowledge of the ASR or speech contents is required during the training or inference stages. Moreover, the effectiveness of this approach extends to different datasets without necessitating the fine-tuning of the bridge module, ensuring efficiency and improved generalization.