Transport and spin relaxation characteristics of the conduction electrons in silicon samples doped with bismuth in the 1.1·10¹³ - 7.7·10¹⁵ cm^-3 concentration range were studied by the Hall and electron spin resonance spectroscopy. Hall effect measurements in the temperature range 10-80 K showed a deviation from the linear dependence of the Hall resistance in the magnetic field, which is a manifestation of the anomalous Hall effect. The magnetoresistance investigation shows that with current increasing magnetoresistance may change its sign from positive to negative, which is most clearly seen when the bismuth concentration goes up to 7.7·10¹⁵ cm^-3. The conduction electron spin relaxation rate dramatically increases in silicon samples with sufficiently low concentration of bismuth ~ 2·10¹⁴ cm^-3. All these results can be explained in terms of the concept of spin-dependent and spin flip scattering induced by heavy bismuth impurity centers.