This study presents a Bayesian approach to enhance the magnitude spectra of single-channel reverberant speech signals. Speech dereverberation model is constructed by using a nonnegative convolutive transfer function (NCTF) and a nonnegative matrix factorization (NMF). NCTF is used to characterize the magnitude spectra of speech signal and room impulse response while NMF is applied to represent the fine structure of speech spectra. Importantly, we deal with the variations of dereverberation model by introducing the exponential priors for reverberation kernel and noise signal. A full Bayesian solution to speech dereverberation is obtained according to the variational Bayesian inference algorithm. Using this algorithm, the room configuration and the speaker characteristics are automatically learned from data. Such a general model can be reduced to the previous methods. Experimental results on both simulated data and real recordings from 2014 REVERB Challenge show the merit of the proposed method for single-channel speech dereverberation.