It's really up to you. You could tell someone you're trying to find a sponsor, and ask if they would be willing to meet with you to see if you're a good "fit" for each other. Or you could just invite someone for coffee, see how things go and then ask if she'd be willing to sponsor you.
The thing is, you can't take a "no" as a personal rejection. Some people feel they don't have enough to offer as a sponsor (e.g., they haven't worked the steps formally, themselves, with a sponsor--which should be a prerequisite), some are too busy with other commitments (including, maybe, too many others they are sponsoring), and for some, they may like you a lot but just feel that it wouldn't be a good "fit."
But most people are very honored to be asked. And if the person you ask isn't available, you can ask them if they have any suggestions as to who might be a good sponsor for you.