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Bayesian empirical likelihood (BEL) method with missing data depends heavily on the prior specification and missing data mechanism assumptions. It is well known that the resulting Bayesian estimations and tests may be sensitive to these assumptions and observations. To this end, a Bayesian local influence procedure is proposed to assess the effect of various perturbations to the individual observations, priors, estimating equations (EEs) and missing data mechanism in general EEs with nonignorable missing data. A perturbation model is introduced to simultaneously characterize various perturbations, and a Bayesian perturbation manifold is constructed to characterize the intrinsic structure of these perturbations. The first- and second-order adjusted local influence measures are developed to quantify the effect of various perturbations. The proposed methods are adopted to systematically investigate the tenability of nonignorable missing mechanism assumption, the sensitivity of the choice of the nonresponse instrumental variable and the sensitivity of EEs assumption, and goodness-of-fit statistics are presented to assess the plausibility of the posited EEs. Simulation studies are conducted to investigate the performance of the proposed methodologies. An example is analyzed. Propose a Bayesian local influence to assess the effect of various perturbations.Introduce a perturbation model to simultaneously characterize various perturbations.Construct a Bayesian perturbation manifold to characterize the structure of various perturbations.Develop the adjusted local influence measures to quantify the effect of various perturbations.Present goodness-of-fit statistics to assess the plausibility of the posited EEs.