We present the results of investigation of high-field (up to 40 T) galvanomagnetic effects in bicrystals of semimetalic Bi and 3D topological insulator Bi1−x Sbx (0.07 < x <0.22) with nano-width crystallite interfaces (~100 nm). At B>2T directed along the interface plane in the quantum oscillations spectrum of Bi and Bi-Sb bicrystals, two new harmonics have been detected. Their periods of oscillation characterize the much larger cross-sectional areas of Fermi surface of charge carriers than it is in single crystalline specimens. In small disorientation angle Bi bicrystals of an inclination type, a number of Hall quasi-plateaus were observed, which vanish by reversing the magnetic field. It has been also found that in bicrystals of Bi-Sb with small crystallite disorientation angle, the semiconductor-semimetal transition is induced in crystallites and interface layers at different values of magnetic field.