Fano resonances of bilayer graphene could be attractive for thermoelectric devices. The special profile presented by such resonances could significantly enhance the thermoelectric properties. In this work, we study the thermoelectric properties of bilayer graphene single and double barrier structures. The barrier structures are typically supported by a substrate and encapsulated by protecting layers, reducing considerably the phonon thermal transport. So, we will focus on the electronic contribution to the thermal transport. The charge carriers are described as massive chiral particles through an effective Dirac-like Hamiltonian. The Hybrid matrix method and the Landauer-Büttiker formalism are implemented to obtain the transmission, transport and thermoelectric properties. The temperature dependence of the Seebeck coefficient, the power factor, the figure of merit and the efficiency is analyzed for gapless single and double barriers. We find that the charge neutrality point and the system resonances shape the thermoelectric response. In the case of single barriers, the low-temperature thermoelectric response is dominated by the charge neutrality point, while the high-temperature response is determined by the Fano resonances. In the case of double barriers, Breit-Wigner resonances dominate the thermoelectric properties at low temperatures, while Fano and hybrid resonances become preponderant as the temperature rises. The values for the figure of merit are close to two for single barriers and above three for double barriers. The system resonances also allows us to optimize the output power and the efficiency at low and high temperatures. By computing the density of states, we also corroborate that the improvement of the thermoelectric properties is related to the accumulation of electron states. Our findings indicate that bilayer graphene barrier structures can be used to improve the response of thermoelectric devices.