[EDIT: I didn't say that you ARE needy, only that perhaps TO HER specifically you could be coming off that way. Most people would be fine with what you're doing and not feel crowded at all but it's possible that SHE feels this way. That wasn't meant to offend you, honestly, nor was it said in a harsh manner.]
It sounds to me as if you're investing a lot into this new adult friendship, and it's very possible that you're coming off as needy and demanding of her time. I don't think you're being silly but I do think that you're over-thinking her actions and her in-actions. I think you're crowding her. I think your expectations of her are very high, and other people don't always work on our own timetables.
So she initially told you "no" on the whatever thing with the bus and then ended up signing up for it. You wanted her to e-mail you personally one-on-one but don't have that same expectation of the other parents? That's not reasonable. Especially since you don't know how they, as a family, came to change their minds. You're not entitled to that process nor to immediate personal notification.
You're making a big deal out of small non-issues and you're not giving her the benefit of the doubt. I do think you need to lighten up a bit and not take things so personally since this is a very new friendship. I also think that perhaps because your girls are all such good friends, you might be pushing this woman a little too hard to be YOUR BFF.
For now, set some boundaries for yourself and lower your expectations. I have a neighbor friend who treated me as if we knew each other our entire lives as soon as I moved to the neighborhood and frankly, I didn't like her right away. I wasn't ready to "be that close" with her. I've been here nearly 7 years and it's taken some training for her not to be so intrusive, but we're better friends for it. I needed her to learn to back off and lower her expectations on what I was "supposed" to do as a friend and what she could realistically ask of me. Of course the reverse was true as well for me.
It sounds as if this women is making effort to be friends, and that she's not snubbing you at all.