She may have low self esteem and feels that she would be a bother to you. Don't try to avoid her. If you should catch her eye, smile and say "How are you?" Then look away just to let her know you have no animosity. If the frost melts, then you may be a little friendlier.
However, if she sniffs and looks away hastily and haughtily. You know she is no friend of yours. At that point you can avoid her as well or you can ask her if you have somehow offended her. Some gossip may have misinformed her about you. This will give you an opportunity to clear the air.
At any rate, don't waste time thinking unpleasant thoughts. Live and let live.