We present an experimental verification of the novel approach to the excitation of surface plasmon resonance (SPR) for biosensing applications. The technique is based on a bent SMF28–type single-mode optical fiber with a thin metal film deposited on its optical cladding. Due to the bending of the fiber, strong coupling can be achieved between the fundamental mode and the surface plasmon mode through the intermediary of whispering gallery modes supported by the fiber cladding, which brings about a resonant dip in the transmission spectrum of the fiber. Since the propagation constant of the surface plasmon mode depends strongly on the refractive index of the surrounding medium so does the coupling wavelength, which enables precision refractometry both in the wavelength and intensity-modulated regimes. As opposed to traditional optical fiber-based SPR refractometers, our approach, while based on a standard single-mode fiber, needs neither additional optical elements (such as long-period or tilted Bragg gratings, etc.) nor mechanical modification of the fiber (such as chemical or mechanical removal of a part of optical cladding). This makes the proposed refractometer structurally simple, reliable, and easy to fabricate.