Along with urbanization and the deployment of GPS sensors in vehicles and mobile phones, massive amounts of trajectory data have been generated for city areas. The analysis of these data has substantially contributed to research and advancements of travel time estimation. However, existing work focuses on estimating travel time inside a particular area, and cross-area travel time estimation has privacy security challenges due to data exchange issues among areas. Meanwhile, the majority of methods estimate a deterministic travel time for a given trajectory, which does not account for complex traffic situations and user requirements. To address these problems, we propose a cross-area travel time uncertainty estimation algorithm for estimating the uncertainty of travel times while preserving privacy among different areas. Specifically, we design a comprehensive cross-area privacy-preserving solution that trains a tailor-made neural network travel time estimator in each area by local data, and incorporates federated learning for training. Furthermore, we employ Bayesian deep learning principles and adopt Monte-Carlo dropout to quantify the uncertainty associated with travel time. To evaluate the proposed approach, we conduct a series of comprehensive case studies with two real-world trajectory datasets. Extensive results demonstrate the superiority of the proposed approach compared to baselines in the context of the cross-area setting.