Current social recommendations based on Graph Neural Networks (GNNs) often neglect to extract rating bias from user and item statistics, leading to misinterpreting real user preferences. For example, a high rating from a user with lenient rating standards and a high average rating does not always indicate a real preference for the item. This situation highlights inherent flaws in existing recommendation algorithms that do not adequately account for bias in user and item ratings and rating trends. To address this problem, this paper proposes an enhanced social recommendation method based on GNNs with integrated rating bias offsets (SR-BS). Firstly, we obtain rating bias from users and items by subtracting their average rating value from the historical rating value for each user/item. To enhance the model’s learning capability, we transform the rating biases into vector representations. Secondly, in the model learning, diverse meta-paths are predefined for modeling interaction relations between graph nodes (e.g., user–item–user, user–user). The aggregation of semantic information from these relational paths is achieved by stacking multiple GNN layers, enabling the fusion of higher-order information. Finally, the experimental results on four datasets—Ciao, Epinions, Douban, and FilmTrust—show that our method outperforms other state-of-the-art methods in social recommendation tasks, exhibiting high stability and personalization.