Dear A,
Congrats on scheduling the call. It is not always easy and proves that you have good communication skills.
I am gonna give you some tips that have worked great for me in the past, and I expect them when I have calls with people who would like to work for BCG.
1. Start by presenting yourself in 1-1,5 minutes. Keep it short and keep it interesting. You will need it for your interviews as well, so please prepare this.
2. Ask very specific questions. Don't start by saying that you just wanted to meet them and make it seem like a casual chat. Consultants are super busy and want to interact with people who know what they want and need. Otherwise, they'll feel that you're wasting their time.
3. They know you need a referral so please don't make it awkward and ask for it. They'll most probably offer to do it if they like you. If you really want to ask though, frame it like this “Do you think that a referral is a must in order to have my CV reviewed, or can I just submit my application on the website and still have a chance to be considered”? By this sentence, you give them the chance to kindly offer you the referral.
4. Keep it as short as possible. When you don't have something else to ask, then just be honest about it and say that you don't have any more questions and that you really appreciate they took the time to talk with you.
5. Show that you understand how busy they are and make very clear how thankful you are they devoted their time to answering your questions.
6. After your call, send a follow-up thank you message.
If you anything else, I will be more than happy to help. Just send me a pm.
Best of luck with everything:)