I remember maybe five years ago my neighbor's 2 boys was playing outside one afternoon and I just happened to be out there. Now these kids are at least 5 or 6 years younger than myself. For some reason they showed a strange interest in asking me to join them in their games. We would play for hours, until the sun went down if I recall correctly. It was okay...for the first few days...
But then it became a
constant everyday thing. Worst of all, I got really tired of playing outside with them doing the same exact stuff (now that I look back I think we did practicularly nothing but talk about bugs and stuff). They were even coming in MY yard waiting for me to come out! Soon, I just stopped going outside at all, doing all I could to avoid contact with them. At that time I didn't know how to tell them that I didn't want to play outside with them anymore. I don't know what they thought of me then (or now). It's not that I didn't like the kids, but I really weren't interested in playing outside with them for hours and hours anymore.
But don't let that discourage you
I say go for it. Sure you may not have the same interests but the way I look at it you could learn different things from each other. But as it was mentioned, I wouldn't just ignore her because then she may think of you in a negative way. If I thought to do it then, I may have talked more with those two boys about what things I was interested in doing (which may have included whether or not I felt like playing outside).
Give it a try. And be honest in your conversations to each other so that there are no pressumptions or any misunderstandings. If it turns out that you two are too different to become good friends then so be it. If you two find that you have some really good times together then you both gain a new friend!