The spin texture of the spin-split surface states on Bi(111) has been comprehensively investigated by high energy and angular resolution spin- and angle-resolved photoelectron spectroscopy. A large out-of-plane spin component that alternately changes its sign is clearly observed. There is no evidence for peculiar polarization oscillation of the in-plane spin component, which was suggested to be due to breaking of the time-reversal symmetry in a previous report [A. Takayama et al., Phys. Rev. Lett. 106, 166401 (2011)]. The observed band structure and spin polarization are well reproduced by the $kp$ model Hamiltonian considering the ${C}_{3v}$ crystal symmetry, and the in-plane polarization variation at the different $k$ points can be understood by the photoemission final-state effect.