I think she's being flirty and playing hard to get. If she had of said "No, I have to [insert lame excuse here]," then it would have been a brush off. It sounds like she's wanting you to try harder. What try harder means varies from girl to girl. That's where you've got to know something about her and her likes and dislikes. It could be cycling, or eating cookies you fixed yourself, or whatever she takes as a romantic encounter. I don't think she wants you to give up. Just make sure you don't throw yourself at her. If you look like you're too easy to please, then she'll lose interest too quickly. We don't appreciate what comes too quickly.
I think if I were in your shoes, I would try "I (we) are going to ___________ on Saturday. Would you like to come?" Say it like she's welcome, but you're going regardless of what she does. That make get her interest up. If you look too easy to get, she'll lose interest very fast.
