I, too, am one of the painfully shy people. A therapist once told me she thought I had a social anxiety disorder. It's not that I can't make friends or am an unfriendly person, per se. It's just that much harder for someone like me to chit-chat, particularly with people that I don't know all that well (such as neighbors). Answering the phone or making phone calls is insanely difficult for me. I get nervous, my heart pounds, I try so hard to say the right things that don't sound stupid. It's a big ordeal!
Believe me, your relationship with her is not one-sided! Your kindness does not go unnoticed. As you continue to be nice and open, she will eventually open up (if she's anything like me). But please don't judge her because if she senses that she's being judged, she will close right back up (again, if she's anything like me). If she senses that you're only talking to her just to "be nice" and not because you actually want to be there, she's not going to open up. It is very hard for people like me to make friends (mostly because I assume that people just small-talk with me out of obligation, rather than an actual desire to talk to me), but once we do, we are very loyal!
I know it's just an example, but quite frankly, I'd like to be the kind of wife that dresses up for her husband (as opposed to the yoga pants I'm usually in)! It's like getting ready for a night on the town, but just for your husband. It doesn't mean HE demands it...maybe it's something she really enjoys doing because she sits at home all day with her kids just playing, cooking, cleaning, laundering, getting grungy and just wants to feel pretty for few minutes with her man. Nothing wrong with that (unless he's a royal a**).
Keep trying. She may be wishing for a neighborly friendship as much as you...it's just 800 times harder for her.