Motivated by the excellent electronic properties of theoretical proposed monolayer boron monosulfides (BS) binary materials, which belong to a light-element member of the group IIIA chalcogenides family, we have investigated the electron and phonon transport properties of three monolayer phases of BS (alpha, beta and gamma) using first-principles and Boltzmann transport theory methods. The calculated electronic structures show that alpha- and beta-BS are semiconductors with indirect bandgaps of 4.01 eV and 3.87 eV, respectively, whereas the gamma-BS is a semiconductor with a direct bandgap of 2.97 eV. Additionally, due to their light carrier effective masses, superior high carrier mobilities are observed, thus bringing high Seebeck coefficients. We also find that due to the absence of imaginary phonon frequencies, the three monolayer phases of BS show dynamical stability. The phonon group velocity and relaxation time are also calculated to analyze the phonon thermal conductivity. We find that strong phonon scattering makes gamma-BS monolayer possess extremely low phonon thermal conductivity (1.2 and 2.7 Wm(-1)K(-1) along the x and y directions at 300 K, respectively), whereas alpha- and beta-BS monolayers show a relatively high phonon thermal conductivity. Therefore, the highest predicted ZT value of 1.7 (n -type) at 700 K is obtained for monolayer gamma-BS along the x direction. However, alpha- and beta-BS monolayers have extremely low ZT values. Our results reveal that the gamma-BS monolayer has wider promising applications in high performance thermoelectric material than alpha- and beta-BS monolayers.