In i-vector based speaker recognition systems, back-end classifiers are trained to factor out nuisance information and retain only the speaker identity. As a result, variabilities arising due to gender, language and accent ( among many others) are suppressed. Inter-task fusion, in which such metadata information obtained from automatic systems is used, has been shown to improve speaker recognition performance. In this paper, we explore a Bayesian approach towards inter-task fusion. Speaker similarity score for a test recording is obtained by marginalizing the posterior probability of a speaker. Gender and language probabilities for the test audio are combined with speaker posteriors to obtain a final speaker score. The proposed approach is demonstrated for speaker verification and speaker identification tasks on the NIST SRE 2008 dataset. Relative improvements of up to 10% and 8% are obtained when fusing gender and language information, respectively.