We present the mechanical, electronic, optical and thermoelectric behaviors for BiBO3 and BiAlO3 perovskite crystals, which are investigated by employing density functional theory (DFT). The structural and elastic characteristics are computed by using GGA-PBEsoI exchange-correlation functional, while the electronic, optical and thermoelectric properties are derived through modified Becke-Johnson (mBJ) potential. The thermal stability is calculated by using the enthalpy expression and further verified by the elastic properties. Besides the physical properties at the ground state, we also explore the effects of pressure (0-40 GPa) onBiBO(3) and BiAlO3, in strides of 10 GPa, on the electronic structure. Both BiBO3 and BiAlO3 illustrate indirect band gap (Gamma-M) at 0 GPa, however, increase in pressure results in transforming to a direct (Gamma-Gamma) band gap at 20 GPa and 40 GPa, respectively. Under the application of pressures, complex dielectric constant and some other optical parameters are also inspected. All the computed optical properties have revealed a higher energy shift, as the applied pressure increases proposing potential optoelectronic device applications of BiBO3 and BiAlO3. Finally the thermoelectric characters are elucidated by calculating the electrical conductivity, thermal conductivity and the Seebeck coefficient of BiBO3 and BiAlO3 compounds, which are discussed as a function of temperature. These compounds are prospective applicants for the optoelectronics and thermoelectric devices, due to their appropriate direct bandgap nature realized by applying pressure and the optimum exhibited thermoelectric behaviors, respectively.