first, ask few simpler questions after shiur – see if like how they answer you and see if like their hashkafa and way talk during shiur, if can be good match for you. then pick one. then, depending on you or your circumstances, can say: i have some questions, and was wondering when or if you have any time that i can call you or meet you. or can ask if you can help with kids or cooking for shabbos, etc. (this works well in eretz yisroel, don’t know how well it goes in ny. out of town could definitely work).
i was never the type to do this – but once heard a rav speak, and he said one should do this – so, i said to myself, okay, i’ll do it to your wife – it’s your own fault. other person – should have done it much sooner – never met her, but everyone told me that i’m very similar to her; once finally met her, we clicked.
if in end, you feel it’s not the right person, you didn’t lose out at all. anyways, sometimes different people are experts for different types of questions. one person i get more chinuch banim from. another more haskafic issues.
most rebbetzins who give shiurim would actually love to develop kesher with others. just may not have time. if that’s the case – be creative – how about walk her back to her car or where she lives, etc.
good luck! it’s scary, but soooo important. will make tremendous difference in your life.