The sad truth is that she is going to have far more political capital in the company than you, so you shouldn't make this a management issue - it's too trivial an issue, and you will be seen as a troublemaker, or childish.
Because of the nature of your conversation (not personal), and since the floor plan is open-floor she may feel as if listening in/jumping in is appropriate. Clearly it makes you feel uncomfortable, especially if she simply stares, without actually saying anything.
That really can only mean one of 3 things:
- She either feels left out/ is lonely
- She is giving you a hint to stop talking
- She simply enjoys making you feel uncomfortable and watching you
There are ways to discourage her, or change her behavior, you just have to be patient and work at it for a little while.
The next time she's staring at you politely ask her if you can help her. Simply turn from the person you're speaking with, look her dead in the eye, and without any frustration, or anger say something along the lines of:
insert name here, I can see you are following our conversation. Did you want to jump in?
Excuse us, insert name here, are we bothering you?
These lines have the advantage of putting the onus on her to justify her behaviour. Her response will determine how you must steer the conversation from there.
a) If she's simply lonely, try to include her into some conversations some of the time. Maybe even engineer some conversations purely for her sake. It's worth getting her on your side, if she stops bugging you the rest of the time.
b) If she responds in a nasty, or mean way, saying something to the effect that "the rest of us here are working, you know", then you may want to consider your own actions. Do other people around you talk as much as you do? Are they as loud?
If you're not the problem, and she's being nasty for no good reason (maybe she does it too, or is even louder), then reply along the lines of:
We didn't mean to disturb you. Perhaps you could be a little more understanding, it's just the nature of the office design that our conversation isn't more private.
c) If she's simply enjoying making you feel miserable, then simply call her on it. Every time she stares, ask if you can help her. If she makes a tasteless comment, put her on the spot:
If you "stay classy", you will garner everyone else's support. If an issue eventually does reach the manager, you will have others be able to testify that you acted professional and courteous at all times.
However, if you are going to chat about TV shows, and sport's matches, maybe get up and walk over to the water cooler? Or reserve those conversations for when you're waiting around the coffee machine?
Chances are that if this conversation reaches your manager she might be able to say that you waste time talking / are disruptive, and have a case for it. The manager will always tend to want to get this type of person out of their hair and simply reprimand you.
If, however, you remain polite and she continues her behaviour, THEN you have a case for approaching the manager, describing the situation, and asking for an intervention:
Boss, I want to bring something to your attention that I was hoping I would be able to deal with myself. I know that the open-floor design doesn't afford people a lot of privacy, and I'm ok with that, however I've been encountering some situations that make me very uncomfortable, and have been persisting over a long period of time. Whenever someone stops over at my desk to give me some files, or say hello (always say the work related version first), insert name here turns around and stares at us. I typically make sure that if I'm having a private conversation I restrict it to around the water cooler, or the coffee machine, so I don't feel that I'm being very disruptive. I tried to defuse the situations by trying to include her into the conversations, or asking if we are bothering her, but she just makes petty, mean comments, that I feel are inappropriate. etc etc etc.