It’s your job to pursue your mentor, not the other way around. Take the initiative to start the conversation. Be willing to try again if you don’t succeed the first time. Show how you can add value to that person.
When a mentor does say yes, you may need to be creative in finding a time for you both to meet. Do you live in the same city and can connect during a morning jog? Does a 30-minute monthly video call work better? Find what works for both of you.