I think it really depends on what exactly you are looking for in a Mentor.
There are several websites that offer Mentoring services free of charge for members, and that can be a good place to start.
I would say that finding someone that is willing could be tough if you just "cold call", since it might just come as a complete surprise that someone would want them to be a mentor without them having offered to do so.
Probably the best place to start is on one of the translation websites where they offer the service... You browse through the people offering to be a Mentor and check out their profiles. From there you can see if you find someone that matches with your philosophy, or your work ethic, or your language pairs, or you think they have something to offer.
One major point a lot of people get hung up on is "Language Pair". I personally have mentored people that do not work in my pairs, since I don't provide language-related mentoring. I focus on practical aspects of getting yourself out there, selling yourself, having a good profile and a good CV, taking the right training courses, not getting ripped off by "special offers" or finding yourself getting roped into scams or long test translations that never lead anywhere (except to frustration, of course).
As I said, it is all about what you want from the relationship... I think it is important to know where you want the relationship to go, what the goals are (for both mentor and apprentice). Do you want language mentoring? business? specific skills? specific fields of expertise? All that is going to condition who you get in touch with and how.
I think it is best to get in touch with a couple of people, either "cold calling", going in to an agency, getting on a translator website, etc., and from there, test the waters, see how you feel corresponding with these people... If there is no rapport, there will not be a good mentoring relationship.
Remember that the idea is that someone is going to give you ahelping hand getting started, not load you down with pro-bono work so that you can "progress" (their career, not yours LOL) and "improve" (their bank account balance).
If you are not enjoying it, something is wrong.