Edge transport bifurcation induced by external biasing is explored with self-consistent turbulence simulations in a flux-driven system with both closed and open magnetic field lines. Without bias, the nonlinear evolution of interchange turbulence produces large-scale turbulent eddies, leading to the high levels of radial transport in the edge region. With sufficiently strong biasing, a strong suppression of turbulence is found. The plasma potential structures are strongly modified with the generation of sheared mean flows at the plasma edge. Consequently, the turbulence-driven flux is decreased to a much lower level, indicating a transition to a state of reduced transport. The simulations show that the dynamics of the phase and amplitude of fluctuations play a crucial role in the mechanism of transport suppression driven by biasing.