We report bilayer-graphene field effect transistors operating as THz broadband photodetectors based on plasma-waves excitation. By employing wide-gate geometries or buried gate configurations, we achieve a responsivity $\sim 1.2V/W(1.3mA/W)$ and a noise equivalent power $\sim 2\times 10-9W/Hz-1/2$ in the 0.29-0.38 THz range, in photovoltage and photocurrent mode. The potential of this technology for scalability to higher frequencies and the development of flexible devices makes our approach competitive for a future generation of THz detection systems.