In this paper, we investigate the possibility to excite Bloch surface waves (BSWs) on the tip of single-mode optical fibers. Within this framework, after exploring an idealized, proof-of-principle grating-coupling-based scheme for on-tip excitation of BSWs, we focus on an alternative configuration that is more robust with respect to fabrication-related non-idealities. Subsequently, with a view towards label-free chemical and biological sensing, we present a specific design aimed at enhancing the sensitivity (in terms of wavelength shift) of the arising resonance with respect to changes in the refractive properties of the surrounding environment. Numerical results indicate that the attained sensitivities are in line with those exhibited by state-of-the-art plasmonic bioprobes, with the key advantage of exhibiting much narrower spectral resonances. This prototype study paves the way for a new class of miniaturized high-performance surface-wave fiber-optic devices for high-resolution label-free optical biosensing, and represents an important step forward in the ``lab-on-fiber’’ technology roadmap.