We present a novel monolithic coupling method for analysing the dynamics of active contractile surfaces in biological systems. Unlike previous models with explicit coupling, our method overcomes stability issues for large surface viscosity. The approach integrates hydrodynamics of surface and bulk fluids in a single finite-element system, incorporating a chemical species to regulate active stress, inducing spontaneous pattern formation. Numerical tests demonstrate stability, also for high surface viscosity. Additionally, we introduce a reduced model for cases with dominant surface viscosity, which solves the hydrodynamics only along the surface. We demonstrate how the reduced computational costs of the proposed methods enable efficient three-dimensional simulations.