Multiple-input multiple-output (MIMO) is a key ingredient of next-generation wireless communications. Recently, various MIMO signal detectors based on deep learning techniques and quantum(-inspired) algorithms have been proposed to improve the detection performance compared with conventional detectors. This paper focuses on the simulated bifurcation (SB) algorithm, a quantum-inspired algorithm. This paper proposes two techniques to improve its detection performance. The first is modifying the algorithm inspired by the Levenberg-Marquardt algorithm to eliminate local minima of maximum likelihood detection. The second is the use of deep unfolding, a deep learning technique to train the internal parameters of an iterative algorithm. We propose a deep-unfolded SB by making the update rule of SB differentiable. The numerical results show that these proposed detectors significantly improve the signal detection performance in massive MIMO systems.