Blackbeard is going for Buggy now that he knows he is no longer protected by the World Government.
This may even be the reason for the confrontation between Blackbeard and Shanks that Oda teased in Marineford.
We must remember that Blackbeard is not like Luffy. Blackbeard does not care about freedom and adventures. He has a goal: to become the Pirate King and he will do everything to get there.
For instance, if Blackbeard was in Luffy’s position with Rayleigh in Sabaody, he would have asked him where is Laugh Tale whereas Luffy refused to hear anything.
So, this means that Blackbeard is probably not the type of guy who would chase all four Road Poneglyphs, manage to read them and then eventually would find Laugh Tale. If there was an easier way to reach the place, he would take it without thinking twice.
But who knows how to go to Laugh Tale? The Roger Pirates only. But all of them are among the best pirates of all times… except one: Buggy.
Unfortunately, Buggy was a Warlord from the moment Blackbeard became a major player to chapter 956, meaning he was protected by the World Government. Capturing him at that time would have been too dangerous. But now, there is a weak pirate in the New World and Blackbeard believes he knows where Laugh Tale is (even if the reader is not sure about this part).