It could be she just wants to keep it casual, talk to you every so often but I don't think, as you say she's busy, she'd spend her time calling you if she didn't like you? She may not have time to go out and do anything, may want to just keep it phone occasionally, don't know. But it doesn't hurt to have a "plan" for when she calls next time so you can make a deliberate, "how about next Wednesday evening. . . " proposition. If she wiggles out of it and doesn't help make an alternate plan then that's okay, at least you'll know.

I don't think there's anything pathetic about your response; I never even dreamed of asking people to do things. I still remember when I was 20 and a woman 3-4 years older than I was, a family friend's daughter whom I knew but she was leagues "better" than I was stayed with us one night and we were supposed to share my double bed but she went to bed first and was taking up a lot of space so I just decided to sleep on the floor/rug rather than push her over and my mom got really mad, said I'd embarrassed the girl, etc. No way I could have asked someone to do something with me.