Spin injection and detection in bulk GaN were investigated by performing magnetotransport measurements at low temperatures. A non-local four-terminal lateral spin valve device was fabricated with Co/GaN Schottky contacts. The spin injection efficiency of 21% was achieved at 1.7 K. It was confirmed that the thin Schottky barrier formed between the heavily n-doped GaN and Co was conducive to the direct spin tunneling, by reducing the spin scattering relaxation through the interface states.