We demonstrate control by applied electric field of the charge states in single self-assembled InP quantum dots placed in GaInP Schottky structures grown by metalorganic vapor phase epitaxy. This has been enabled by growth optimization leading to suppression of formation of large dots uncontrollably accumulating charge. Using bias- and polarization-dependent micro-photoluminescence, we identify the exciton multiparticle states and carry out a systematic study of the neutral exciton state dipole moment and polarizability. This analysis allows for the characterization of the exciton wave-function properties at the single-dot level for this type of quantum dot. Photocurrent measurements allow further characterization of exciton properties by electrical means, opening new possibilities for resonant excitation studies for such systems.