Hesitation is a great thing to have: you look twice before crossing a busy street; you double check lists; you ask an extra question before agreeing.
Hesitation doesn't work as well when seeking a mentor.
Too often, we find ourselves waiting for the 'perfect' mentor... or the right moment to approach someone... or just until we have an 'in' ... or the right introduction. Any number of things can have us talking about how great having a mentor would be and even more reasons why we haven't asked someone yet.
Yes, sometimes a great opportunity will present itself if you wait patiently. More often than not, you need to create that opportunity. What's the worst thing that can happen? They might say no. (gasp) But no one will think less of you for asking.
We only hold ourselves back when we don't ask for what we want or need. Hesitation helps us evaluate risk; don't use hesitation to avoid doing something that carries much more benefit than downside.