Personalized product search that provides users with customized search services is an important task for e-commerce platforms. This task remains a challenge when inferring users' preferences from few records or even no records, which is also known as the few-shot or zero-shot learning problem. In this paper, we propose a Bayesian Online Meta-Learning Model (BOML), which transfers meta-knowledge, from the inference for other users' preferences, to help to infer the current user's interest behind her/his few or even no historical records. To extract meta-knowledge from various inference patterns, our model constructs a mixture of meta-knowledge and transfers the corresponding meta-knowledge to the specific user according to her/his records. Based on the meta-knowledge learned from other similar inferences, our proposed model searches a ranked list of products to meet users' personalized query intents for those with few search records (i.e., few-shot learning problem) or even no search records (i.e., zero-shot learning problem). Under the records arriving sequentially setting, we propose an online variational inference algorithm to update meta-knowledge over time. Experimental results demonstrate that our proposed BOML outperforms state-of-the-art algorithms. © 2022 ACM.