We investigate the intrinsic spin dynamics of electrons bound to Al impurities in bulk ZnO by optical spin noise spectroscopy. Spin noise spectroscopy enables us to investigate the longitudinal and transverse spin relaxation time with respect to nuclear and external magnetic fields in a single spectrum. On one hand, the spin dynamic is dominated by the intrinsic hyperfine interaction with the nuclear spins of the naturally occurring 67Zn isotope. We measure a typical spin dephasing time of 23 ns, in agreement with the expected theoretical values. On the other hand, we measure a third, very high spin dephasing rate which is attributed to a high defect density of the investigated ZnO material. Measurements of the spin dynamics under the influence of transverse as well as longitudinal external magnetic fields unambiguously reveal the intriguing connections of the electron spin with its nuclear and structural environment. © 2013 American Physical Society.