The current stability studies of the hydraulic turbine regulation system (HTRS) mostly adopt the linear hydro-turbine model ignoring its strong nonlinearity, leading to insufficient disclosure of the true characteristics of the HTRS and also causing great inconvenience to the controller parameter tuning. To address this issue, based on the Hopf bifurcation theory, bisection method, and stability criterion, this paper proposes an algorithm (HBBSC) for determining the controller parameter constraint considering the nonlinearity of the hydro-turbine. Firstly, the nonlinear model of the hydro-turbine is constructed based on the model reconstruction strategy (NNGW) combining the backpropagation neural network (BPNN) with the improved grey wolf optimization algorithm (IGWO) to obtain an accurate nonlinear HTRS numerical simulation platform under the power control mode (PCM) and frequency control mode (FCM). Then, the HBBSC-based quantitative calculation procedure of stability region constraint is introduced in detail. Further, in a case study of stability region calculation of HTRS, the HBBSC is applied to calculate the stability region constraint, and the HBBSC-based stability region is verified through a simulation platform. Finally, the stability region of complex HTRS under all operating conditions is calculated based on HBBSC. The results indicate that the HBBSC can replace the traditional methods for stability region calculation during stability analysis of HTRS, outperforming the latter in accuracy and reliability.