We obtain here an approximate, nonlinear Fokker-Planck-type equation which offers an improved model for two-dimensional nonequilibrium, bistable flows driven by exponentially correlated Gaussian noise. The new model accurately predicts the renormalization of the phase-space statistical densities P(x,v) with correlation time. The theory is tested for accuracy by both analog electronic and digital simulations of a damped oscillator with a bistable potential, driven by additive, colored noise. For large noise strengths, the improved theoretical scheme is applicable for small noise correlation times tau, but becomes increasingly better for small noise strengths where its accuracy extends even tolarge noise correlation times. The crossover to overdamped motion is also discussed.