Should I tell my boyfriend?

My ex and I parted a few years ago and last year became friends again, in fact best friends. Him and I did minor stuff, but broke off the friendship right after. (we got to 2nd base). My bf knows everything and already expressed that he was not quite fond of him due to our history and all the sh*t he did to me. I'm a pretty nice person and I avoid drama by being nice to everyone. My ex recently has been trying to get close yet again and I can't just turn him away. I'm too nice to do so! Anyways my ex told me my bf is bad to me (even though he isn't) and how my bf will hurt me. He basically told me to end things with him. I wanted to handle the situation myself but I can't stop it. I haven't told my bf about what my ex has said (this all happened in the last couple days) but I'm thinking I should now. Should I tell him or should I keep trying to resolve it myself. My bf hates drama as do I by the way.