We propose a method that computes bounds on the group betweenness centrality (GBC) of groups of vertices of a network. Once certain quantities related to the network are computed in the preprocessing step that takes O(n(3)) time, where n is the number of vertices in the network, our method can compute bounds on the GBC of any number of groups of vertices successively, for each group requiring a running time proportional to the square of its size. Our method is an improvement of the method of Kolaczyk et al. [Social Networks, 31, 3 (2009)], which has to be restarted for each group making it less efficient for the successive GBC computations. In addition, the bounds used in our method are stronger and/or faster to compute. Our computational experiments show that in the search for a group of a certain size with the highest GBC value, our method reduces the number of candidate groups substantially and in some cases the optimal group can be found without exactly computing the GBC values which is computationally more demanding.