In this work, a new approach based on the use of a one-dimensional photonic crystal (1DPC) made of dielectric layers with alternating refractive indexes deposited inside a photonic crystal fiber (PCF) is proposed as a suitable platform for the excitation of Bloch surface waves (BSWs). The presence of an additional dielectric layer on the 1DPC modifies the local effective refractive index, enabling a direct manipulation of the BSWs. In particular, we investigate BSW resonance conditions in a 1DPC of alternating layers of TiO2 and SiO2 deposited inside a three-hole suspended-core PCF to design an ultra-wide range refractive index sensor in the near infrared. The obtained simulation results indicate that BSW sensors based on PCF could be an alternative to surface plasmon resonance (SPR) sensors, with a ultrahigh sensing figure-of-merit, which might facilitate applications in high-resolution refractive index sensing.