I am the Former Shyest Person on the Planet too, and I find it very nice of you, ZachHart72, that you care about making them feel comfortable!
In my school years I talked to NOone and if someone talked to me, I got very panic. Such an invitation like Angela said would have made me freak out, lol. If you invite them to a coffee, make sure they know you have a time limit, that's an excellent idea! so they know, they will be dying at most for half an hour
I would say, give them a feeling that they are totally ok like they are. You don't need to say it, they will feel it. Just send a signal "you're ok, everything's ok". Don't stare at them, look away, and if you talk, talk about yourself first.
Why not sit down near them without talking till they are more familiar with you? Like doing homework together or sitting in the classes together or in the library? Just ask if it's ok you're sitting there, smile at them from time to time and don't talk. With time, they will get used to you and some day talk by themselves.
If you really find them ok like they are, and they are shy, don't force them to communicate. Isn't it great to spend time with them even when they don't talk? I don't know, but that's how it worked with me...