Unlike in conventional semiconductors, both the chemical potential and the band gap in bilayer graphene (BLG) can be tuned via application of external electric field. Among numerous device implications, this property also designates BLG as a candidate for high-performance thermoelectric material. In this theoretical study we have calculated the Seebeck coefficients for abrupt interface separating weakly- and heavily-doped areas in BLG, and for a more realistic rectangular sample of mesoscopic size, contacted by two electrodes. For a given band gap ([Formula: see text]) and temperature (T) the maximal Seebeck coefficient is close to the Goldsmid-Sharp value [Formula: see text], the deviations can be approximated by the asymptotic expression [Formula: see text], with the electron charge -e, the Boltzmann constant [Formula: see text], and [Formula: see text]. Surprisingly, the effects of trigonal warping term in the BLG low-energy Hamiltonian are clearly visible at few-Kelvin temperatures, for all accessible values of [Formula: see text] meV. We also show that thermoelectric figure of merit is noticeably enhanced (ZT > 3) when a rigid substrate suppresses out-of-plane vibrations, reducing the contribution from ZA phonons to the thermal conductivity.