Will she be using your facility at the exclusion of anyone else training at that time? I am assuming that you exclusively do personal training at your facility and that you do not have other trainers working out of your studio. Otherwise, I would charge her a similar fee.
You could also ask what her budget is for the use of the studio. Then decide the amount of time you are willing to allow her to have based on that amount.
I also would not be comfortable allowing her to use the gym unsupervised. Since I would feel the need to be present, I would consider that in my pricing as well. With that in mind, I would probably charge her my lowest rate for personal training a client.
If I had met this person and had a good feeling about them, I might just charge a small fee just to make it a business deal, as a professional courtesy. I would still have her fill out all the usual forms, waivers, etc.