Pathways for enhancing the thermoelectric performance of bismuth at low temperatures are explored. These include applying an external magnetic field and nanostructuring. We present a theory describing the anisotropic thermoelectric properties of bismuth in terms of carrier effective masses, scattering, and band-structure characteristics obtained from experiment. It is found that the magnetic field or nanostructuring, when applied separately, can lead to significant improvements in the thermoelectric figure of merit. However, despite their beneficial yet different effects on the transport, it is shown that applying simultaneously a magnetic field and nanostructuring is not a feasible way of improving the thermoelectric performance of bismuth.