Software Defined Networking (SDN) offers Traffic Engineering (TE) great flexibility by decoupling the control and data plane. As network services become more diverse, the single-domain control architecture is no longer sufficient to meet scalability requirements, and the multi-domain and multilevel distributed control architecture is gaining popularity. However, traffic engineering across multiple domains poses challenges, particularly when each administrative domain is unwilling to disclose its network topology and resource information due to privacy concerns. To address this issue, this paper adopts the concept of differential privacy and perturbs the domain information to achieve bandwidth indistinguishable TE. Unfortunately, perturbations may decrease the accuracy of the TE algorithm's resource allocation, negatively affecting performance. To mitigate this problem, we propose BI-TE, which utilizes a GNN-based bandwidth utilization prediction model to assist the controller in selecting the optimal forwarding path, thereby enhancing TE efficiency. Experimental results demonstrate that compared to abstraction-based hierarchical TE, BI-TE can reduce the processing time by nearly 24.35% while ensuring network bandwidth utilization close to 90%. Additionally, the fairness of allocation is also guaranteed.