Speech enhancement (SE) utilizing diffusion models is a promising technology that improves speech quality in noisy speech data. Furthermore, the Schrödinger bridge (SB) has recently been used in diffusion-based SE to improve speech quality by resolving a mismatch between the endpoint of the forward process and the starting point of the reverse process. However, the SB still exhibits slow inference owing to the necessity of a large number of function evaluations (NFE) for inference to obtain high-quality results. While Consistency Models (CMs) address this issue by employing consistency training that uses distillation from pretrained models in the field of image generation, it does not improve generation quality when the number of steps increases. As a solution to this problem, Consistency Trajectory Models (CTMs) not only accelerate inference speed but also maintain a favorable trade-off between quality and speed. Furthermore, SoundCTM demonstrates the applicability of CTM techniques to the field of sound generation. In this paper, we present Schrödinger bridge Consistency Trajectory Models (SBCTM) by applying the CTM's technique to the Schrödinger bridge for SE. Additionally, we introduce a novel auxiliary loss, including a perceptual loss, into the original CTM's training framework. As a result, SBCTM achieves an approximately 16x improvement in the real-time factor (RTF) compared to the conventional Schrödinger bridge for SE. Furthermore, the favorable trade-off between quality and speed in SBCTM allows for time-efficient inference by limiting multi-step refinement to cases where 1-step inference is insufficient. Our code, pretrained models, and audio samples are available at https://github.com/sony/sbctm/.