This seems like one of those, "If you have to ask, you aren't ready" type of questions to me.
Of course it is a two way street, the mentor would have to want it as well, but in my experience (which is pretty limited) just asking someone to teach goes a long way. Lots of people love teaching a younger generation and would see such a request as a compliment, rather than being selected for a 'job' to perform.
And being selected out of the large number of available choices would only further increase the value of that compliment.
Think of it as a dating problem: You have to choose a mentor that is not so busy that they won't be able to teach you, and on the other hand of a sufficiently advanced level compared to your own in the fields that you feel that you are lacking in that you can be taught. And then there has to be a certain chemistry, without that it won't work either.
Asking about that problem is totally valid. I haven't a clue how to go about finding an answer but I don't think that the question needs to be placed in the 'if you have to ask you aren't ready' category, in fact there are very few such questions.
There are no stupid questions, there are only stupid answers, and questions that were never asked.