Thephenomenonofstochasticresonance(SR)inabistablenonlinearsystemisstudiedwhenthesystemisdrivenbytheasymmetricpotentialandadditiveGaussiancolorednoise.Usingtheunifiedcolorednoiseapproximationmethod,theadditiveGaussiancolorednoisecanbesimplifiedtoadditiveGaussianwhitenoise.Thesignal-to-noiseratio(SNR)iscalculatedaccordingtothegeneralizedtwo-statetheory(shownin[H.S.WioandS.Bouzat,BrazilianJ.Phys.29(1999)136]).WefindthattheSNRincreaseswiththeproximityofatozero.Inaddition,thecorrelationtimeτbetweentheadditiveGaussiancolorednoiseisalsoaningredienttoimproveSR.TheshorterthecorrelationtimeτbetweentheGaussianadditivecolorednoiseis,thehigherofthepeakvalueofSNR.