A calculation of the non-singlet part of spin dependent structure function, xg N S 1 (x, Q 2 ) and associated sum rule, the Bjorken Sum rule up to next-next-to-leading order(NNLO) is presented. We use a unified approach incorporating Regge theory and the theoretical framework of perturbative Quantum Chromodynamics. Using a Regge behaved model with Q 2 dependent intercept as the initial input, we have solved the Dokshitzer-GribovLipatov-Altarelli-Parisi (DGLAP) evolution equation up to NNLO at small-2 ) and the solutions are utilised to calculate the polarised Bjorken sum rule(BSR). We have also extracted the higher twist contribution to BSR based on a simple parametrisation. These results for both of xg2 ) and BSR, along with higher twist corrections are observed to be consistent with the available data taken from SMC, E143, HERMES, COM-PASS and JLab experiments. In addition, our results are also compared with that of other theoretical and phenomenological analysis based on different models and a very good agreement is also observed in this regard. Further a very good consistency between our calculated results and theoretical QCD predictions of BSR is also achieved.