As I talked to the technical director in a cantina event, chat bubbles are an absolute nightmare with this game. It caused all sorts of issues/lag in beta when they had them and until they figure out how to fix the technical errors that arise when putting chat bubbles, we are not going to see them. Sorry it's just the truth. It's not on their list of priorities right now for the game but he said they are always figuring out how to do things. Maybe, just maybe if they "crack the code" so it doesn't cause the lag they might be able to do it.
I wouldn't hold my breath though. Sorry!
Funny thing, I also spoke to him at the NYC Cantina Tour last October, and they said we will be seeing them when they fix the issues, and that it is a thing they are actively working on and a relatively high priority for the UI people.