Chat bubbles were slated to be in the game, in fact they were in beta but due lag issues they were removed. In fact they were still in the game files after launch and you could modify your game files so that you could see chat bubbles but that has since been removed.
It is a bit ridiculous that this game doesn't have something as simple and universal as chat bubbles and the swtor community would like an answer as to when they are going to be put back into the game.