My advice? If she shows interest in someone else, do the same. There are a lot of reasons why.
1) She may be testing your interest in here, if they do it this soon, pass on her.
2) Show confidence, chicks dig confidence. If you look like a simpering pup who's emotions are at her whim, she likely wont stay interested.
3) You might meet someone awesome...always a plus.
4) You look like a hot commodity when you garner interest from other women, hence making you a more coveted romantic interest for her, may pull her to you better.
5) Dont let you happiness depend on just one person. You are more likely to meet the best match for yourself when you are not in "persue" mode. You tend to act different while in that mindset and may not attract someone good for you (they will be interested in the act you put on...and may not like the "settled" you...this is a big reason why so many marriages fail these days).
Whatever you do, keep open with them. Keeping your line in the water isnt something you are doing to hurt or manipulate them, it is something you are doing to ensure whoever you pair yourself with in life is the best of your options...and you should hope the best for them as well.
Ive had a handful of female friends I was interested in, but I can proudly say the first and only woman I have ever dated and been in love with is the same one I am with over 11 years later. Interestingly enough, it wasnt an existing female friend, but someone who I met when a female friend who was interested in me said to me one day "Ive never seen you hit on a girl...why dont you try it."
Best of luck to you. Hope it helps.