Bayesian inference for ERGMs is a doubly-intractable problem because of the intractability of both the likelihood and posterior normalizing factor. Auxiliary variable based Markov Chain Monte Carlo (MCMC) methods, such as exchange algorithm, has been adapted to the Bayesian inference for ERGMs, is asymptotically exact but computationally demanding and require extra tuning. In this work, we propose to convert the Bayesian inference into estimation of conditional expectations, where we first sample from the joint distribution of parameters and data, then construct optimal predictions of any functions of model parameters via kernel regression. We use adaptive importance sampling which greatly improves the efficiency of sampling step. This method by design is concentrated on approximation of posterior moments but can be up to orders of magnitude faster than MCMC, and is flexible to accommodate all kinds of state-of-the-art prediction techniques. We show the usability of the presented approach using real social network data and compare their accuracy and efficiency with results obtained based on the most recent version of approximate exchange algorithm implemented in Bergm package.