I got an offer from Bain by considering the following specialties of Bain (besides the usual requirements for top tier consultancies):
1) Bain is the challenger in the McK/BCG world - position yourself accordingly
Bain is still smaller and in most markets considered as the challenger. This requires to 'get more out of less' and to be more in an exploration rather exploitation mode. Generally speaking this will leave room for creativity and innovation also from Associates/Consultants (while e.g. McK most topics would be already explored). Thus, focus on your strong drive to push new topics and your creativity and first principles thinking that you will leverage for the upcoming cases.
2) Bain is willing to fostering their offering around 'Digital' - tweak your story accordingly
In my understanding, Bain is pushing the Digital portfolio quite strongly. Tweaking your story on what you did around that topic (maybe e.g. work on organizational culture during your university?) might help to emphasize your ability to push the company forward on that frontier - however, more a plus than a requirement.
3) Bain is looking for strong personalities - reflect before your interview on yourself
Bain is a creative companies, very much focusing on strong personalities who are well reflected and are sure about their "Why" (e.g. what is the deep drive behind choosing a certain type of internship in your CV). Ask yourself "Why" multiple times for each of the steps of your CV beforehand, in order to provide a certain depth within the interview.