When we place microphones close to a sound source near other sources in audio recording, obtained audio signals include undesired sound from the other sources, which is often called bleeding sound. For many audio applications including onstage sound reinforcement and sound editing after a live performance, it is important to reduce the bleeding sound in each recorded signal. However, since microphones are spatially apart from each other, typical phase-aware blind source separation (BSS) methods cannot be used. We propose a phase-insensitive method for blind bleedingsound reduction. This method is based on time-channel nonnegative matrix factorization, which is a BSS method using only amplitude spectrograms. In the proposed method, a gamma prior distribution is introduced for the frequency-wise leakage gains of the bleeding sound component to estimate the mixing matrix. This estimation can be interpreted as maximum a posteriori probability estimation. From the experimental results, it is confirmed that the proposed method can reduce the music bleeding sound with higher accuracy than the other methods in both simulated and real situations. It is also confirmed that the proposed method achieves robust performance against parameter initializations, which is an important advantage in practical applications. The reason of this robustness is experimentally revealed.