Just be honest with her. "Hey, I'm not great at keeping conversations going and it causes me some anxiety. I really want to get to know each other and don't want you to misinterpret any silence as lack of interest."

Most people would be very understanding about something like that, if you show some vulnerability and honesty.

Also, consider getting one of those packs of questions that are intended for couples to get to know each other. It's a fun game to play, just answer a few of the questions together and relax.