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Bimodal distributions of protein activities in signaling systems are often interpreted as indicators of underlying switch-like responses and bistable dynamics. We investigate the emergence of bimodal protein distributions by analyzing a less appreciated mechanism: oscillating signaling systems with varying amplitude, phase and frequency due to cell-to-cell variability. We support our analysis by analytical derivations for basic oscillators and numerical simulations of a signaling cascade, which displays sustained oscillations in protein activities. Importantly, we show that the time to reach the bimodal distribution depends on the magnitude of cell-to-cell variability. We quantify this time using the Kullback-Leibler divergence. The implications of our findings for single-cell experiments are discussed.