Ditto everything Megan C says. I swear, I could be your friend. And it is not because I don't care, it is just because I am a terrible initiator. I'm not even that busy. But like Linda, it is hard for me to reach out sometimes. I am not shy, but have a hard time being the lead in a friendship until we have been friends for a while, because of my insecurities. I dread the idea of being the needy friend. That is all my own fault, and if you are uncomfortable "carrying" the friendship, then it is your right to stop being the one who always invites. But you might very well lose this friend because she doesn't want to be the agressive one. I am always thrilled to get an invitation, and love the friends I have, but even though I assume they feel the same way, I still can't bring myself to call them constantly or whatever. Part of that is just that I am a terrible phone person. I actually have one needy friend (she knows she is) and I have just told her that I am bad on the phone and bad at inviting, but that it isn't personal. I have to remind myself to make an effort with her every once in a while so that she doesn't start thinking I am mad at her and get upset. But when I do make the effort, I make sure to tell her it isn't her, just my own issues. It's actually proving to be good for her to realize that she doesn't have to freak out when people don't call her everyday.
I also have a horrible schedule. I don't think to call people until late at night. That is when I am up because I never sleep, but I realize that other people go to bed at a normal hour. So I don't let myself call people, because I will never assume my hours are the same as someone else's.
I think being upfront is the best idea. Just ask if you are being too needy or if her schedule is too busy right now. That would totally make me realize that I was doing my usual thing of sitting back and waiting for friends to come to me. I'm afraid that if you send a too-vague message to her to test how she will respond, she will also respond vaguely and you will think she isn't interested. I realize that it sounds stupid to say someone is afraid to respond too enthusiastically to a point-blank invitation, but it happens. Common sense says that if they are inviting, they are interested in being friends. But inside my brain common sense doesn't always prevail with things like this. I think if she was not interested she would not answer your calls. Or like the other poster said, if she was the type who just can't say no, you would see it in her behavior. No one spends hours talking over lunch with someone they don't get along with. Now, if you don't want to deal with an insecure friend and always have to take the lead, that is totally understandable. But if you like her, I wouldn't write her off just yet. And now that I have written all this out and realized how silly my behavior is sometimes, I think I will call my friend and invite her to lunch tomorrow. I need to work on doing that...