Advice needed! (Boyfriend's ex)

My boyfriend and I have known each other for 6 years. We recently started dating and I knew his ex she's a nice girl. I have no problem with I wouldn't say we are friends but I knew her when she was dating my current boyfriend. They dated for 4 years it was a pretty serious relationship. But it didn't work out my boyfriend broke up with her because he didn't love her any more. We started dating 5 months after they broke up. We have been together for a year now. And his ex is still in love with him. She messages him on social media texts him on a daily basis. He tells her to move on its been a year she even messages me about how she loves him and how they have history. She shows up at bars that she knows we will be at. I'm not a fighter at all I never be mean to her I just ignore her all together. My boyfriend and I don't know what to do, Any advice?