I think these are really good suggestions, BeagleMommy.
Without knowing all the details, backstory, social dynamics of your office or all the people, I have the impression that annoying co-worker is trying (too hard!) to befriend you. Again, it's just a theory and without knowing all that other stuff I can't back up what I'm saying. It's just an impression I have.
Is she very young? Because maybe she just doesn't know how to make appropriate small talk with office mates. I'm trying to think about what's underlying her behavior with the intention of trying to figure out a longer-term solution, because I think I have read that she's done stuff like this lots of times in the past. Was there an incident where she kept badgering you about eating bagels that she ordered just for you? Or was that a different thread by a different member of the board?
Because this lady sounds like she is either very immature (and I'm not trying to be ageist here, really. I know a lot of people in their early 20's who are social experts!) and just doesn't know yet the nuances of office communication, or she could just be really clueless, or even have certain other social anxiety issues which I cannot get into without getting the thread locked.
Unless you want to take the time to get to know her and maybe "mentor" her in terms of office etiquette (and it sounds like you really don't - not that I blame you), maybe the best thing to do is respond in the manner suggested by the PP's in this thread here...like, every. single. time. you interact with her. You know, like kind of give her the cold shoulder and only interact with her when your job requires you to do it...maybe she will eventually get the hint, (some people never do) and if not, at least maybe trying to "reach out" to you will be so unfruitful/unpleasant that she will cease the annoying behavior. I mean, I don't know if you can come right out and confront her about her communication style...I don't think it would work. It sounds like this is just her personality and she maybe thinks she is being cute or charming.
I guess it's best to just try to limit your contact with her as much as you can. This sucks, BeagleMommy. You sound like such a warm and kind person - maybe she sees that in you and is trying to reach out but just doesn't know how to do that effectively. Or, maybe she knows you don't like her much and she's overcompensating, thinking if she just tries harder you'll like her and everything will be wonderful, only you're just not interested. I've seen it happen.