Nonnegative matrix factorization (NMF) is developed for parts-based representation of nonnegative data with the sparseness constraint. The degree of sparseness plays an important role for model regularization. This paper presents Bayesian group sparse learning for NMF and applies it for single-channel source separation. This method establishes the common bases and individual bases to characterize the shared information and residual noise in observed signals, respectively. Laplacian scale mixture distribution is introduced for sparse coding given a sparseness control parameter. A Markov chain Monte Carlo procedure is presented to infer two groups of parameters and their hyperparameters through a sampling procedure based on the conditional posterior distributions. Experiments on separating the single-channel audio signals into rhythmic and harmonic source signals show that the proposed method outperforms baseline NMF, Bayesian NMF and other group-based NMF in terms of signal-to-interference ratio.