A standard single-mode optical fiber, coated with low-index polymer (Cytop), then a thin Au sheath, immersed in fluid, is proposed as a structure for optical (bio)chemical sensing. The highest-order EH1m cladding modes are found to couple strongly to long- or short-range surface plasmons on the Au sheath, forming coupled modes that are sensitive to the refractive index of the fluid or to a biochemical adlayer formed on the outer surface of the Au sheath. Interrogation of the modes can be achieved with the help of a tilted grating photoinduced into the core of the fiber. We demonstrate experimentally, in this manner, the excitation of these modes, and their use for bulk sensing. Furthermore, negative bulk sensitivity was observed for some leaky modes beyond cutoff.