In this paper we present experimental study of electron-nuclear spin dynamics in GaAs bulk layers doped with Mn ions at temperature 4.2 K. The electron spin dynamics is experimentally investigated by measuring the degree of  polarization of photoluminescence in a transverse magnetic field (Hanle effect) and the recovery of the electron spin polarization in a longitudinal magnetic field (polarization recovery curve). To study nuclear spin dynamics, we use two-stage experimental protocol including optical cooling of nuclear spin system and measuring change of the polarisation degree of photoluminescence in different transverse magnetic fields. We show dependence of electron spin relaxation times on excitation power for three samples with different concentrations of shallow donors and acceptors. Electron spin relaxation times have been obtained as at the exciton transition as at the deep acceptor Mn transition. Also we show dependence of nuclear spin-lattice relaxation times T1 on value of external transverse magnetic field.