My boyfriend is bisexual

So my boyfriend and I had been dating for four months when he told me he was bisexual. We had already said "I love you" by this point and I felt really hurt that he kept it from me. I felt like he'd been lying to me for our whole relationship! I also felt really insecure that I'd have to compete with both genders now and that he'd probably cheat on me cuz now everyone is my competition. Was I right to be mad and hurt by it? I don't think he'd cheat on me but I was feeling really bad about the whole thing and really hurt by all of it.