Mentors are overrated in software development.
Certainly, if you can find someone who really knows what they're doing and who is willing and has time to help you improve your programming skills, you'd be foolish not to take advantage of their help. Some organizations try hard to set up those kinds of relationships, both to help you become more productive and also to keep an eye on what you're producing.
However, I think it's much more common that people learn from a variety of sources, including:
teammates: not just a single mentor, but everyone you work with
code reviews: there's nothing like having your code (or even someone else's) picked over by a group to sharpen your sense of what's considered good and not good in your organization
existing code: the more time you spend maintaining other people's code, the more you'll learn how to (and how not to) write your own code
books: reading is fundamental
internet: reading blogs and sites like Programmers.SE and Stack Overflow will expose you to lots of opinions about the "right" way to do things, and you'll start to develop your own opinions
experience: most important; you really can't appreciate the benefits and/or drawbacks of a given idea unless you try it out; write lots and lots of code
friends: having some friends who are also programmers is a huge help even when they're not your "mentors" but just people to chat with
If you can learn from some or all of these sources, having a mentor is helpful but not required for you to improve your skills.
If you want to climb the corporate ladder more quickly, talk to your supervisor about what you need to improve. Make it clear that you're working hard to improve, and show them that helping you improve will be worthwhile. You may be able to take classes, go to conferences, connect with other developers in the company, etc.