You said you are meeting her for two Fridays now. How long has it been since you have a feeling for her? Spend more time with her, say 3-4 more meetings and if you convinced at that stage go ahead and tell her directly.

I maybe wrong here, but I feel you are just hot on it now. Give yourself some time to be sure as if you tell right away, it can have a bad effect not just on your possible relation but also on a budding friendship.