We present a mean-field theory for spiking networks operating in the balanced excitation-inhibition regime, with synapses displaying short-term plasticity. The theory reveals a novel mechanism for bistability which relies on the nonlinearity of the synaptic interactions. As synaptic nonlinearity is mainly controlled by the spiking rates, the different states are stabilized by dynamically generated changes in the noise level. Thus, in both states, the network operates in the fluctuation-driven regime, producing activity patterns characterized by strong spatiotemporal irregularity.