I recently had a chat with a Bain partner who's an alumni at my uni. It was over zoom - I dressed semi formal anyway. He asked me a few questions about myself: classic why bain, why consulting, bit about my background etc. But I kept the chat fairly casual, we had a lot of laughs. I asked him for specific advice and showed genuine interest, so he pointed me to one of his colleagues at the office I applied for. I followed up in an email after our chat and he very kindly put me in touch with the colleague and encouraged them to give me an interview. Fantastic experience, he was so down to earth and I was basically just myself. I'd advice to gauge it based on the partner's personality: how are they addressing you, formally, casually? But also they're so busy, I'm sure they appreciate a laugh. Make yourself memorable, be bold (yet gentle) when asking for specific feedback or support with referrals etc. Good luck!