Why does she still stare at me if she rejected me three months ago?

About three months ago I approached a young lady at work. I politely asked her out and I politely accepted her rejection like a gentleman. She told me she was seeing someone. However, after a week I could not take the pain/hurt of rejection. Instead of a normal greeting I just went over to where she was got what I needed from her at work and simply said thank you with a withdrawn demeanor. However, I did not berate her or insult her. I simply did not exchange hellos or how are yous with her. It has been about three months and things are becoming normal, pre-rejection. Since I have been on “moving on mode” since the rejection I noticed she stares at me and quickly looks away when I catch her looking at me. Why does she do this? Also, prior to asking her out, for about a year, once a month I would throw a compliment her way and even flirted with her a little bit. Is it strange nowadays that after a guy pursues a woman for a year, all of a sudden holds his horses when she says no? Do most guys just insult a girl that rejects them or become persistent? I did not do either of those? I remained polite after rejection(except for a few days where I did not even greet her), but have not shown anymore interest. I wonder what her stare means? Do most guys just become jerks after rejection like hostile and do some become persistent? What course should I still take if I am still interested? I don’t have the emotional fuel in my heart or my head to stay on the saddle and then be hurt again when she says no. Ladies please help me here.