Just had a game last night that exemplifies what can be done with a culture bomb. I play BtS 3.19 where the culture bomb is reduced from what it had been in earlier patches. Even so, here is what happened; Settled two new cities, and allowed 20 or so turns to pass. A GA popped and, a few turns later, Music tech, so another popped up. Culture bombed both cities with the GAs. The effect on both borders was phenomenal. The resultant border pop extended WAY out past the BFCs of both cities, out to a 3, and in some cases, a 4 tile radius. In this way, several relatively distant resources were suddenly within my cultural borders. Rushed workers to the sites, built the mines/camps/plantations rapidly, and now had a number of valuable additions to the trade list, enabling some new trades which immediately provided health and happy bonuses. In addition to the resource and trade enhancements, these greatly extended borders effectively prevented any AIs from slipping in and settling in places I deemed undesirable.
Love this game.