A comprehensive experimental study of a fiber optic relative humidity (RH) sensor is carried out in terms of characterization and performance optimization against various parameters that affect the sensor response and sensitivity e.g., film composition, film thickness, fiber core diameter, and the sensor geometry. The sensor is based on evanescent wave absorption spectroscopy and utilizes a specific reagent immobilized permeable polymer membrane cladding on a declad U-bend optical fiber. An optimum film thickness and an optimum film composition exist. In addition, a fiber with a smaller core diameter was observed to be more sensitive, unlike the previously reported results. The sensitivity further increases with a decrease in the bending radius. The sensor is found to be sensitive to RH ranging from ~1.6 to ~92%, exhibiting a very fast response time, an extremely good degree of reversibility, repeatability, and a large dynamic range.