I'm dealing with something similar but with a long time "friend." I'd known her since childhood and she always got in little digs and insults and then would laugh and say "I'm just teasing." But I don't do that to her. And none of her other friends do either. If she thought they were so funny, wouldn't she surround herself with people who did that too?
I finally gave her the cut direct. And it's a big deal because we'd been close friends for years. And she sent me a similar email wondering why I was mad at her. She had been rather nice at some point and in the past few years she was really mean. And yet she doesn't know? I find that hard to believe. But I don't know.
I'm like you, OP. I would be hurt if someone were avoiding me, but I'd take the hint. I wouldn't chase them down and beat them over the head to find out what happened.
Ultimately, you just want her to leave you alone, right? You don't owe her to teach her that she's aggressive or gossipy. Definitely don't invest a lot of time in a reply, no matter what you do. Either completely delete all her texts (in fact, see if you can block them before your receive them) and ignore, ignore. Or write a short, terse reply like "I used to be friendly and neighborly. But you talk rudely behind my back and you do it to others, too. You're a bully and pushy. I don't care to spend a lot of time with you. I wish you well. Please, stop contacting me" and then ignore, ignore.