  Millikelvin magnetotransport studies are carried out on heavily $n$-doped
wurtzite GaN:Si films grown on semi-insulating GaN:Mn buffer layers by
metal-organic vapor phase epitaxy. The dependency of the conductivity on
magnetic field and temperature is interpreted in terms of theories that take
into account disorder-induced quantum interference of one-electron and
many-electron self-crossing trajectories. The Rashba parameter
$\alpha_{\text{R}}\,=\,(4.5 \pm 1)$ meV$\AA$ is determined, and it is shown
that in the previous studies of electrons adjacent to GaN/(Al,Ga)N interfaces,
bulk inversion asymmetry was dominant over structural inversion asymmetry. The
comparison of experimental and theoretical values of $\alpha_{\text{R}}$ across
a series of wurtzite semiconductors is presented as a test of current
relativistic ab initio computation schemes. It is found that electron-electron
scattering with small energy transfer accounts for low temperature decoherence
in these systems.
