You are on point in saying that Bain put less emphasis on fit interviews compared to McKinsey and BCG, especially on the first round.
Their focus is really on assessing candidate's logical prowess and structured thinking capacity through case interviews. It is just very recently that they started to add a bit of fit questions (or PEI questions as per McKinsey's term) on their early stages.
Based on my previous experience interviewing with Bain (which was around 45-60 minutes), they spent only a fraction of the interview time on first round (around 5-10 mins) having a fit discussions. The questions are quite standard, such as 'why Bain?', 'why this specific offices/ region?', ' what's your short-term and long-term goals?', 'how Bain fits with your goals?'.
There is little possibility of deep dive PEI interviews focusing on the topics of conflict management or leadership experiences as will likely be the case in McKinsey and BCG interviews.
However, it wouldn't hurt prepared a bit of anecdotes just in case if they are asking a curve ball questions involving these topics. Even then, most likely they will just asking to check without deep diving further into the details.
The last 5-10 mins are left for Q&A. For this one, do prepare questions that can't be easily found on Bain's websites to show that you have done your research throroughly on the firm.
Hope it helps.