3D instance segmentation (3DIS) is a crucial task, but point-level annotations are tedious in fully supervised settings. Thus, using bounding boxes (bboxes) as annotations has shown great potential. The current mainstream approach is a two-step process, involving the generation of pseudo-labels from box annotations and the training of a 3DIS network with the pseudo-labels. However, due to the presence of intersections among bboxes, not every point has a determined instance label, especially in overlapping areas. To generate higher quality pseudo-labels and achieve more precise weakly supervised 3DIS results, we propose the Box-Supervised Simulation-assisted Mean Teacher for 3D Instance Segmentation (BSNet), which devises a novel pseudo-labeler called Simulation-assisted Transformer. The labeler consists of two main components. The first is Simulation-assisted Mean Teacher, which introduces Mean Teacher for the first time in this task and constructs simulated samples to assist the labeler in acquiring prior knowledge about overlapping areas. To better model local-global structure, we also propose Local-Global Aware Attention as the decoder for teacher and student labelers. Extensive experiments conducted on the ScanNetV2 and S3DIS datasets verify the superiority of our designs.