Bayesian Network (BN) modeling has recently been proposed and utilized in resting-state functional magnetic resonance imaging (fMRI) studies to derive directed connectivity among brain regions in an integrated network. This report focuses on three issues related to the resting-state fMRI BN approach: 1) How the disturbance variable and noise affect BN inference and whether it is reasonable to use extracted fMRI time series averaged over multiple subjects to characterize the effective connectivity common to all of these subjects, 2) the effects of the fMRI time series length (duration) for a given TR(repetition time) on the BN results and 3) the effects of varying the time point at which the data acquisition starts (starting point). Both synthetic dataset and real resting-state fMRI dataset were employed. It is found that the averaged group BN inference is more robust than individual BN inference under most conditions according to the results of synthetic dataset, and the BN structure and parameter estimation are robust to both the variation of the time length (with a minimum) and starting point. Our results might demonstrate the stability of averaged group BN inference on resting fMRI dataset under most conditions, and justify its use to estimate the effective connectivity, which is independent of the start point and the length of resting-state fMRI time series.