In this paper, a theoretical analysis of sensitivity and signal-to-noise ratio (SNR) of a step-index fiber optic surface plasmon resonance sensor with bimetallic layers (silver and gold) has been carried out. The numerical treatment is based on Kretschmann’s SPR theory and Drude model of metals. The light source considered is a p-polarized one. The potential of different bimetallic ratios (gold as outer one) for the sensing purposes has been analyzed. The effect of different design parameters related to optical fiber as well as sensing layer on sensitivity and signal-to-noise ratio of the sensor has been studied. A comparison between selected ray launching and all guided rays launching in terms of sensitivity and SNR has been performed for different bimetallic ratios. The effect of fiber length and FWHM of a Gaussian input on the sensor’s performance has also been studied. All these studies, leads to a significant analysis to achieve the best possible design of a fiber optic SPR sensor with maximum sensitivity and SNR simultaneously for both laboratory and remote sensing applications.