Mentors just kind of sneak up on you. No one ever says, "Hey buddy, want a mentor?" And even though I've heard the advice to come right out and ask someone to mentor you, I can't imagine people actually having that conversation.
In reality, mentoring usually comes in the form of unsolicited advice. You'll be having a conversation and someone will just lay some mentorship on you. So you should be ready for it.
Early in my career as a technical writer for a software company, I was actually doing the job of a systems analyst - designing the system interface instead of writing a user guide explaining how to use the system. Long before I made the move to become a systems analyst myself, I said to one of the bigwigs something about how I should probably learn to program. He said, "Why would you want to do that?" so quickly that I knew he didn't even stop to think - it was a gut reaction. I explained that I thought analysts should know how to program and he said no, they didn't.
Now, if I were really as stubborn in my opinions as some people seem to think I am (Mom) then I would've thought, "well, that's his opinion, but I'm going to do it anyway." And then I would've spent years making myself miserable trying to learn to code. I tried to teach myself in high school and gave up the first time I had to find a bug. I really didn't care enough about it to work at it for fun, so doing it for work would've been agony.
And he was right. It's possible to be a systems analyst without knowing how to code. I did it for years and I was pretty damned good at it.
Now, if I'd wanted to be a programmer, that bigwig might've encouraged me. Or I might have ignored his advice. But I was open enough to consider it.
Years later, I was working at a company that I refer to as The Evil Place because it was so bad that one of my friends/co-workers can't stand to hear the real name of the company. At one point, my manager took me aside and told me that I didn't really have a future with the company (or even hope of getting a promised performance-based bonus) because certain people had developed a negative opinion of me. I began to object, but then she told me that it didn't matter what these people thought of me. We'd worked together at other companies, so she knew that I wasn't the cause of the problem. But she also knew that I was powerless to fix it. After all, I'm not the one who nicknamed it The Evil Place - it wasn't just me.
Again, if I hadn't been open to the advice, my natural need to please everyone would've kicked in and I would still be working there a decade plus later, trying to do such a great job that they had no choice but to acknowledge that I had great technical and people skills. Instead, I accepted that I wasn't going to get anywhere with these people, and got another job.
Even my decision to stop being a techie and become a freelance writer was triggered by some random advice. A co-worker mentioned to me (while we were at the theater waiting for a show to start) that I didn't seem to enjoy working in an office. That nudge set me towards using my technical knowledge and writing skill to write website copy and blog posts, among other things.
I'm not saying that all the advice you get is going to be good. I've gotten some monumentally bad advice over the years and I've even taken it on occasion. But if you refuse to really listen and consider that someone is handing you some primo mentorship, then you're going to miss out.