The influence of lift forces on the dispersion of small bubbles is numerically studied in a homogeneous isotropic turbulence generated by random Fourier modes, under one-way coupling approximation. The effects of bubble Stokes number and mean relative velocity are investigated by computing the statistics from Lagrangian tracking of a large number of bubbles in many flow field realizations, and comparison is provided between the results obtained with and without taking the lift force into account. The effects of preferential concentration, which are known to reduce the terminal rise velocity of bubbles, are also investigated. The lift force is found to drastically modify the correlations and integral time scales of the fluid seen by the bubbles in their fluctuating motion, and to significantly enhance the accumulation of bubbles in high vorticity regions.