Hyperfine resolved electron spin resonance (ESR) measurements of single rubidium (Rb-87) atoms isolated on superfluid helium nanodroplets are presented. In accordance with our previous work on Rb-85, we find a relative increase of the hyperfine constant a(HFS) by about 400 ppm, depending on the size of the droplets. In order to optimize the ESR signal intensities, the processes of optical pumping of Rb atoms on helium droplets and of optical detection of the ESR; transitions are investigated in detail. Both the laser intensity and. polarization influences the ESR signal intensities. A simple model for optical pumping of Rb atoms on helium droplets is presented, which agrees well with the experimental results.