We experimentally demonstrate optical trapping of Rb-87 atoms using a two-color evanescent field around an optical nanofiber. In our trapping geometry, a blue-detuned traveling wave whose polarization is nearly parallel to the polarization of a red-detuned standing wave produces significant vector light shifts that lead to broadening of the absorption profile of a near-resonant beam at the trapping site. A model that includes scalar, vector, and tensor light shifts of the probe transition 5S(1/2)-5P(3/2) from the trapping beams, weighted by the temperature-dependent position of the atoms in the trap, qualitatively describes the observed asymmetric profile and explains differences with previous experiments that used Cs atoms. The model provides a consistent way to extract the number of atoms in the trap.