In this work, we first measure the forward temperature-dependent current-voltage (T-I-V) characteristics of the GaN-based Schottky diodes grown on the bulk GaN substrates, and then study the transport mechanisms of the forward current and the low-frequency current noise behaviors under various injection levels. The results are obtained below. 1) In a forward high-bias region the thermionic emission current dominates, and the extracted barrier height is about 1.25 eV at T = 300 K, which is close to the value measured by capacitance-voltage sweeping. 2) In a forward low-bias region (V < 0.8 V) the current is governed by the trap assist tunneling process, having an ideality factor much larger than 1, and the derived barrier height is about 0.92 eV at T = 300 K, which indicates that the conductive dislocation should be mainly responsible for the excessive leakage current, having a reduced barrier around the core of dislocations. 3) The Lorentzian noise appears only at very small current (I < 1 μA) and low frequency (f < 10 Hz), whose typical time constant is extracted to be about 30 ms, depending on the multiple capture and release process of electrons via defects. 4) At a higher frequency and current, the low-frequency 1/f noise becomes important and the corresponding coefficient is determined to be about 1.1, where the transport is affected by the random fluctuation of the Schottky barrier height.