How long does it take for a bm to understand that I'm not her enemy?

My husband and I have been married for almost 10 years and I am stepmom to his child from a previous relationship. My relationship with my stepchild is wonderful. We get along well and I enjoy being in his life. The only problem is his mother. She's still upset that I as she puts it "Got the ring and the last name when she's the one who has his child." She talks about me to her friends and the child overhears and then he asks me questions. His father told him that his mother and the relationship they had was a mistake BUT he was a BLESSING. I've never said anything shady about his mother because I don't feel the need to. It's been years and my main concern is being happy with my husband. Am I wrong for wanting the mother of my stepson to grow up and let the past go? Am I wrong for thinking that her attitude of being bitter after 10 years is unnecessary? Help me ladies..... I'm just trying to make our blended family work.