Enhanced photorefractive properties of tin hypothiodiphosphate $\left({\mathrm{Sn}}_2{\mathrm{P}}_2{\mathrm{S}}_6\right)$ crystals as a result of Bi doping are presented. These new crystals were obtained by the vapor-transport technique using stoichiometric ${\mathrm{Sn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ composition with an additional amount of Bi up to $0.5\mathrm{mol.}\%$ in the initial compound. The bandgap edges of the obtained crystals are located at $\sim 750\mathrm{nm}$ and shift toward the red wavelengths with increasing Bi concentration. ${\mathrm{Sn}}_2{\mathrm{P}}_2{\mathrm{S}}_6:\mathrm{Bi}$ crystals are found to exhibit larger two-beam coupling gain coefficients (up to $17{\mathrm{cm}}^{-1}$ at a wavelength of $854\mathrm{nm}$ ) as compared to (i) pure ${\mathrm{Sn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ ( $2.5{\mathrm{cm}}^{-1}$ at $854\mathrm{nm}$ ), (ii) ${\mathrm{Sn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ crystals modified by the growth conditions ( $14{\mathrm{cm}}^{-1}$ at $860\mathrm{nm}$ ), and (iii) Te-doped ${\mathrm{Sn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ ( $8{\mathrm{cm}}^{-1}$ at $860\mathrm{nm}$ ). At the same time, for an intensity of $1.3\mathrm{W}∕{\mathrm{cm}}^2$ at $854\mathrm{nm}$ , buildup times of 0.9 and $2.5\mathrm{ms}$ at grating spacings of $\Lambda =9.8$ and $1.3\mu \mathrm{m}$ , respectively, are found; Bi-doped ${\mathrm{Sn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ crystals are the fastest among all the presently known ${\mathrm{Sn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ crystals operating at near-infrared wavelengths.