Terahertz (THz) frequency generation via nonlinear optical techniques is of particular interest due to the immense potential of this type of radiation in various scientific fields, ranging from medicine to telecommunications. Selecting suitable nonlinear media for laser frequency down-conversion presents a challenging task. Considering an approach that uses nonlinear crystals with high radiation resistance, pumped by intense laser pulses near their damage threshold, we suggest the crystal of bismuth triborate (BiB3O6, BIBO). Compared to other borate-class crystals, BIBO exhibits relatively high coefficients of quadratic susceptibility. In this paper, we have studied the optical properties of BIBO samples in a wide spectral range from 0.1 to 2.1 THz at temperatures of 473, 383, 295, and 77 K using Terahertz Time-Domain Spectroscopy (THz-TDS). Furthermore, we simulated collinear three-wave interactions with nonzero efficiency for difference frequency generation (DFG) in the THz range. For the pump wavelengths of about 800 nm, we determined phase-matching (PM) conditions and compared the generation efficiency for different crystal cuts. The potential of utilizing BIBO crystal for terahertz frequency generation is discussed.