I have done a few things with success. On the first day of class, I talk about shyness and other communication differences in my discussion of accessibility. I talk about how gender, race, sexuality, age, etc. affect our capacities and confidence in entering a conversation, and then we talk about how discussion classes often favor chatty folks or assertive communicators smile emoticon. Then, I ask them to come meet with me in private, if they're introverted or have other access needs, and we talk about it. I suggest things that I've done in the past, but I tell them that the first thing is to figure out what is most intimidating about speaking in class (i.e. bad former experiences, fear of being called on unpredictably, fear that creeps in when your hand is raised for too long, or fear of being inarticulate, etc.). Then we tailor a solution (my class always includes nonverbal forms of participation too), and here are a few examples:
1) I will only call on you if you raise your hand.
2) Email me a question ahead of time. I'll ask it, and call on you. No one will know, and you'll have your response prepared so you can speak from notes.
3) I'll call on you immediately if your hand is raised, so you won't lose your nerve.
I tell them to observe my teaching style and build trust. I don't let people dangle smile emoticon. I can spin each comment into something useful. So, if it's a matter of trusting that a prof treats comments respectfully because you've had a negative experience, that trust can only be built with time. So I tell them we can meet in a month and reassess. I tell them that oral participation is important so that other students can gain access to their valuable thoughts. I give them the option of not speaking for the semester, because I give participation credit for visiting office hours, talking to me after class, and active listening, but I try to establish that their comments are vital to collective learning. I spent a lot of time neglecting introverts in my classroom because I misunderstood their lack of participation as a lack of care about the class. That was a shortcoming as a teacher that I've really worked on over the years. In my experience, many shy students don't take an accommodation, but they end up talking anyway, because all they needed was for someone to validate their intelligence and understand that it was more difficult for them than more extroverted students. Hope this helps!
Most importantly (and I didn't say this in the original post), I try to make it clear that the goal is NOT for them to work harder to be more like extroverts. In many ways, that is precisely the cure/rehabilitation model that I try to push against in my pedagogy (i.e. the problematic cultural idea that shyness or introversion is pathological or less valuable than extroversion). Rather, it's to strive for an accessible classroom and pedagogy that encourages students to claim their education (as Adrienne Rich would say!) by figuring out, with me, what they need to grow and flourish.