From the outside, where perspective is maybe clearer, all this is in your head I'm afraid.
She sounds like she's trying to make you a friend, rather than have that awkward silence / outright hostility that being exes can generate. I don't think she's trying to get back together with you at all, and you are just seeing evidence of her genuine affection for you. This is not the same as a desire to be in a relationship with you though!
I know it's hard, but at some point you have to let go and move on. Hell, moping around sniffing after her just makes you less attractive, both to other women and even to her. Sure she may like the ego boost, but it robs you of your masculinity.
Your best course of action, in my opinion, is to remain on speaking terms with her and stop chasing. If she's interested in anything else, she'll chase you eventually, but you really should just get on with your life in case I'm right.