Noisy labeled data is more a norm than a rarity for crowd sourced contents. It is effective to distill noise and infer correct labels through aggregation results from crowd workers. To ensure the time relevance and overcome slow responses of workers, online label aggregation is increasingly requested, calling for solutions that can incrementally infer true label distribution via subsets of data items. In this paper, we propose a novel online label aggregation framework, BILA, which employs variational Bayesian inference method and designs a novel stochastic optimization scheme for incremental training. BILA is flexible to accommodate any generating distribution of labels by the exact computation of its posterior distribution. We also derive the convergence bound of the proposed optimizer. We compare BILA with the state of the art based on minimax entropy, neural networks and expectation maximization algorithms, on synthetic and real-world data sets. Our evaluation results on various online scenarios show that BILA can effectively infer the true labels, with an error rate reduction of at least 10 to 1.5 percent points for synthetic and real-world datasets, respectively.