It's great that you have a chance to talk with Bain partner.
Well, in general, you need to be lightly person on order to do so you need to google the most relevant information about your partner with whom you are going to talk about his background, his competence and focus, past projects. Maybe, you can even find any publications where he was an author. Through this, try to ask him the questions and find similarities with yourself: maybe you cam from the same school, town, or interested in the same topics. This will help you to establish both profesional and personal link.
Listen more than you speak, be an active listener. Partners normally like those person who are smart and listen to them. So make the partner feel great during this conversation. And I'm pretty sure that afterwards he will be eager to help you to get into the firm, which is your ultimate objective.
Hope it helps you,
If you need further tips, just drop me a message,