The aim of our study is to investigate numerically the interaction between a dispersed phase composed of microbubbles and a turbulent Taylor-Couette flow (flow within the gap between two cylinders). We use the Euler-Lagrange approach based on Direct Numerical Simulation of the continuous phase flow equations and a Lagrangian tracking for the dispersed phase. Each bubble trajectory is calculated by integrating the force balance equation accounting for buoyancy, drag, added-mass, pressure gradient, and the lift forces. The numerical method has been adapted in order to take into account the feed-back effect of the dispersed bubbles on the carrying flow. Our approach is based on local volume average of the two-phase Navier-Stokes equations. Local and temporal variations of the bubble concentration and momentum source terms are accounted for in mass and momentum balance equations. A number of reference cases have been tested to validate the modelling approach and its numerical implementation. Then, our previous study of bubble dispersion has been extended to two-way coupling simulations of turbulent Taylor-Couette flows (only inner cylinder is rotating). Modulation of the drag will be discussed for different geometries, Reynolds numbers and bubble sizes. The results show that near-wall turbulent structures are modified by the presence of bubbles.