We describe the results of a numerical and experimental investigation of how a point source of radiation couples light to the HE11 mode of a tapered single-mode fiber. Specifically, we have investigated two different geometries of nonadiabatic, tapered single-mode optical fiber. The motivation for this study is the characterization of a single-mode tapered optical fiber biosensor. In such a device light is collected from fluorescent sources located along the cladding surface of the tapered fiber. Taper-to-taper coupling measurements and fiber mode calculations indicate the device sensitivity decreases exponentially as sources are moved away from the tip of the tapered fiber.