It’s neat that you are getting into UX so early on, lots of opportunity to grow. Starting with startups is definitely a place to start, although slightly more difficult if you do not have much knowledge in the area. Books, online articles, and forums will be your friends!
From my experience there are a few different ways to find mentors, but it does differ depending on where you are from.
My mentors have been those I’ve been working with. They have a lot of knowledge, and are really happy to share it, and because we work together cost comes down to my willingness to learn and apply this knowledge to the work we are completing. Most in the UX community really would like to see it grow and expand, so tend to be willing to share their knowledge, or point you in the right direction.
You can also find communities near you online and ask on them if anyone would be willing to regularly catch up for a coffee, on you generally, to talk about things that you’ve been working on and finding difficult, or any questions you may have.
I’m not sure about the sharing connection, as most of the time mentors are there to help you, but I’m sure you could ask your mentor whether there was anything that you could do to contribute to the relationship as well. It could just be that when you gain enough knowledge you make yourself available to mentor someone :).
Hope this helps.