Measurements of the transverse magnetothermopower and magnetoresistance in single bismuth wires are performed at 80 K. Manifestation of the asymmetry in the magnetothermopower defined as Umkher effect is observed. Investigations of the magnetotransport properties under uniaxial strain reveal a rearrangement of the electronic structure with subsequent changes in the anisotropy of the Fermi surface at high strain rates. A moderate applied strain leads to a decrease in the magnitude of the Umkehr effect in the thermopower up to the vanishing of the effect along the binary axis. The observed behavior of the Umkehr effect is attributed to a decrease in tilt angle φ of electronic ellipsoids under strain, which is consistent with the phenomenological analysis of transport phenomena in bismuth.