When I was in your place, I talked to them about it. The first time we had a long conversation and decided together that it wouldn't be a good thing for either of us because of timing. Later when the timing was better, we did go out for awhile and realized we were better friends. He was a true friend so it never affected our friendship in the long run.
The second time, we talked about it and decided to try it out. We lasted a week and decided we didn't feel that way about each other after all.
I'd consider your options, make a plan, and talk to her about it. You could decide your next course of action together. If she is a true bestie she will understand, and stick around even if you decide not to date. I hope it works out for you! Good luck!