The spin-momentum locking of surface states in topological quantum materials can produce a resistance that scales linearly with magnetic and electric fields. Such a bilinear magneto-electric resistance (BMER) effect offers a completely new approach for magnetic storage and magnetic field sensing applications. The effects demonstrated so far, however, are relatively weak or for low temperatures. Strong room-temperature BMER effects have now been found in topological Dirac semimetal alpha-Sn thin films. The epitaxial alpha-Sn films were grown by sputtering on silicon substrates. They showed BMER responses that are 10^6 times larger than previously reported at room temperature and also larger than that previously reported at low temperatures. These results represent a major advance toward realistic BMER applications. The data also made possible the first characterization of the three-dimensional, Fermi-level spin texture of topological surface states in alpha-Sn.