How do I help my girlfriend get comfortable with role play?

Well sometimes feeling silly is half the fun! I think what you should do is just try it a few times, let her get the feel of it, and then as you do it more and more maybe she will become more comfortable.

If you're doing simple role play like student/teacher or nurse/patient that can be harder sometimes than picking characters and trying to stay in character (or I find it to be) so maybe start with something she is good at. Either characters from a movie she knows well, or if she has a profession or is familiar with one maybe she can slip into that role better

The main thing is to let it feel silly, and take it easy. The above idea about going into simpler roles is good, and don't be afraid to take a break to laugh. After all, if you're not enjoying it, it's not good sex