With the popularity of location-based social networks (LBSNs), users would like to share their check-ins with their friends for more social interactions. These check-in records reflect not only when and where they are, but also what they are doing. If we can capture the relations of the location, time, and activity factors in LBSNs, the location-based social platforms can provide more personalized location-based services to users. In this paper, we aim to infer individual activity and mobility based on their check-in records in LBSNs. For these two inference problems, we analyze check-in records, and utilize Bayesian network to represent the relations among location, time, and activity factors of check-in records. Based on the proposed network model, the two inference problems can be simplified to two modules, the activity-time and the location-activity relation. For the activity-time relation, we propose Order-1 Activity Transition Model to capture the activity-time relations of check-in records. Moreover, for the location-activity relation, we exploit the Gaussian mixture model to capture individual mobility features in different activities. To evaluate the proposed network model for the two inference problems, we conduct extensive experiments on two real datasets, and the experimental results show that our proposed Bayesian-based approach has higher performance than the state-of-the-art approaches for activity and mobility inference in LBSNs.