I cold-messaged both via email and LinkedIn several MBB consultants for an informational chat. A couple days ago I had a phone call with a principal at an MBB firm after cold-emailing her (she is an alumnus at my current university). Although, from my perspective, I asked quite open-ended and well-thought questions which showed interest and answers can't be found very easily by a google search (mostly about personal experiences, differences (pros/cons) to previous jobs she had, focus by office etc.), she seemed quite bored even before we started talking and her answers were relatively short and without much elaboration. After stating that I would like to apply in the next couple weeks etc., she didn't volunteer to have me sent her my CV for a referral, but just said that I should feel free to reach out if further questions come up... Even taking into consideration time constraints MBB consultants have, this was a quite short phone call...
So, my question is: what would your advice be regarding asking "good" questions (=what should the content be?) and the general flow of the conversation? Generally, how high should the expectations for a person to refer me be after accepting a request for a phone call?
Also, at the same firm, I already had a conversation with a Consultant (who has only been at the firm for 3-4 years though) and he told me to send him my CV (implying that he is willing to give me a referral), which I did. Given that he is in a relatively low position and a referral would not have as much weight as principal/partner (although the conversation went quite well), should I continue reaching out to principals/partners or rather leverage my current connection to the consultant and apply via this referral?