A Recommendation system helps filter out items from large amounts of candidates, with the widespread use of these systems, the issue of user privacy protection has become increasingly prominent. At the same time, bundle recommendation tries to further lighten users’ burden, by recommending a group of related items that can be purchased together by the target user, instead of one item at one time. However, existing bundle recommendation methods mainly focus on the accuracy metrics, causing filter bubbles and dissatisfaction. Moreover, existing methods tend to recommend highly popular bundles that may not fit well with the individual needs of users. To this end, this paper introduces serendipity into bundle recommendation and proposes a novel model of Personalized Serendipitous Bundle Recommendation (PSBR). It first extracts the serendipity features of users, bundles, and items by considering the acceptance ability of users, and the coverage ability of items and bundles. Then, it models user preferences by considering user-bundle-item interactions and bundle-item affiliations, as well as captures users’ bias on the bundle size. Finally, it generates proper bundles by combining user preference score, serendipity score, and bundle size bias. Experimental results on two real-world data sets, Steam and Amazon Electronic, validate that PSBR performs better than the most advanced baselines in various indicators. To better protect user privacy while improving the system recommendation system, the datasets used in this paper are anonymized public data. In addition, data protection regulations are strictly adhered to when processing user data to protect the user’s identity from disclosure.