The phase transition properties of Blume-Emery-Griffiths (BEG) model for the spin-3/2 system are investigated on the Bethe lattice (BL) when the system is under the effect of both random crystal field (D) and biquadratic exchange interaction (K). These randomization effects are either turned on with probability 1 - p (q) or turned off with probability p (1 - q) for D and K, respectively. The phase diagrams are obtained on the (K/J, kT/J) and (D/J, kT/J) planes for given values of p and q when z = 3.0 corresponding to honeycomb lattice. Both attractive (K> 0) and repulsive (K< 0) biquadratic exchange interaction values are considered to examine its effects on the BL. It is found that the model presents either second-or first-order phase transitions and also tricritical points. It is also found that the second-order phase lines follow the phase lines of regular spin-3/2 BEG model as K -> +/- infinity for the phase diagrams on the (K/J, kT/J) planes.