Hi Ilya! Welcome
Mentors are really valuable - I myself am one and I have several of my own.
One of my mentees lives overseas (I live in Australia) and we communicate via email. Like anything it can be challenging but nothing that's insurmountable.
One of my mentors lives interstate (Sydney) and another one works two desks over from me right now. For my mentor in Sydney we communicate via google hangouts and over the phone and for my desk buddy we have brief catch ups every two to four weeks. I gain value from all of those conversations regardless of how we have them
I too am an introvert and I also have Asperger's so I totally get the anxiety thing! I've found the easiest way to get a mentor is to just ask them. Find someone that you think will help you with your development need and just reach out to them via email or social media. Most UX people are pretty open to it and will generally only say no if they genuinely don't have time. I took on too many mentees at one point because I wanted to help everyone and I ended up being terrible at it! One of them ended up suffering and I felt terrible so I'm now much more realistic about what I can do for another UXer.
Mentoring is also a two way street so they get something out of it too - think about skills and knowledge that you have that other people might not. When I worked in government I was lacking skills that a more senior designer could mentor me on and he was lacking user research experience so we mentored each other.