In this work, we propose an adaptive set-membership constant modulus (SM-CM) algorithm with a generalized sidelobe canceler (GSC) structure for blind beamforming. We develop a stochastic gradient (SG) type algorithm based on the concept of SM filtering for adaptive implementation. The filter weights are updated only if the constraint cannot be satisfied. In addition, we also propose an extension of two schemes of time-varying bounds for beamforming with a GSC structure and incorporate parameter and interference dependence to characterize the environment which improves the tracking performance of the proposed algorithm in dynamic scenarios. A convergence analysis of the proposed adaptive SM filtering techniques is carried out. Simulation results show that the proposed adaptive SM-CM-GSC algorithm with dynamic bounds achieves superior performance to previously reported methods at a reduced update rate.