A detailed theoretical discussion is presented of the effect of colored noise on nonlinear dynamical systems. The ideas arising from it are applied to a particular example of such a system: a model of dispersive optical bistability, considered in the contexts of both additive and multiplicative forcing. Analogue experiments and digital simulation techniques are used to explore the applicability and range of validity of theories proposed to date. The physical phenomenon of bimodality induced by the finite bandwidth (alone) of additive forcing is demonstrated in detail for the first time. The three existing theories capable of accounting for this phenomenon can each be categorized in terms of a single (constant) value of a characteristic parameter Pexp; but it is shown that, in reality, Pexpt varies weakly with the correlation time tau of the noise. The variation of Pexp, with tau is investigated in the currently accessible range of O.1<tau<infinity.