Stochastic resonance in a time-delayed bistable system subjected to asymmetric dichotomous noise and multiplicative and additive white noise is investigated. We find that the signal-to-noise ratio is a non-monotonic function of the delayed times and of the amplitude of the driving square-wave signal, as well as of the asymmetry and correlation rate of the dichotomous noise. In addition, the SNR varies non-monotonically with the system parameters and the intensities of the multiplicative and additive noise.