Don't assume the billionaire is the best person in general for you to be talking to about your path or next step or he/she will have The Thing for you any more than someone you know very well or in your closer network.
That said if he/she has company(s) then find one you fit best in and perhaps a role that they are looking to fill that you fit well. Then apply for it or reach out to other people that are in that company.
Once you apply or connect THEN ping your billionaire with "hey just wanted to let you know, I've always be intrigued with your success/companies etc and I applied (or trying to connect with) to join...."