Chinese Spelling Check (CSC) aims to detect and correct potentially misspelled characters in Chinese sentences. Naturally, it involves the detection and correction subtasks, which interact with each other dynamically. Such interactions are bi-directional, i.e., the detection result would help reduce the risk of over-correction and under-correction while the knowledge learnt from correction would help prevent false detection. Current CSC approaches are of two types: correction-only or single-directional detection-to-correction interactive frameworks. Nonetheless, they overlook the bi-directional interactions between detection and correction. This paper aims to fill the gap by proposing a Bi-directional Detector-Corrector framework for CSC (Bi-DCSpell). Notably, Bi-DCSpell contains separate detection and correction encoders, followed by a novel interactive learning module facilitating bi-directional feature interactions between detection and correction to improve each other's representation learning. Extensive experimental results demonstrate a robust correction performance of Bi-DCSpell on widely used benchmarking datasets while possessing a satisfactory detection ability.