The best approach I know of, so far, is to offer them something. Ideas probably are the best thing you can bring to their table.
- Look at what the people you consider mentors do, get to know the things they're invested in and brainstorm
- Make a list of 10 ideas for everyone that you would consider to be a mentor
- Mail them the list, explaining that you find them a great person and a valued mentor so far and wanted to give something back
(And they really were mentoring you already, though passively. Keep that in mind.)
These ideas don't have to be overly original or special or genius. Just apply your perspective, take the time to really think it through and find some things you can really stand behind. From full-blown synergies, to minor usability fixes, everything is the right thing.
Why does this work?
This approach works, because even the most succesful, genius person can't think of everything, so they value new stand points, new input. And giving it freely, without strings attached, is a sign of appreciation they probably won't see often, so you stand out from the crowd of either silent admirers or people trying to work an angle.
How would you know?
I'm taking this advice from some, mostly passive, mentors I have, in particular Napoleon Hill, James Altucher and Jerry Colonna, who at some point or another all say this exact thing.