Is it normal that i have a crush on a friend who's bisexual?

So I have a friend who I just met recently in college and I developed feelings for her. One day when we were hanging out she told me that she was bisexual and is currently going out with a friend of mine (who is also female) and to be honest, I felt a bit heartbroken. I really wanted to know her more and be in a relationship but if she's happy with her then I will come to terms and be happy for them. But there's a nagging feeling in my heart, like I can't stop thinking about it. Is it normal for me to have feelings for her even though she's dating someone else? Not to mention, I may have told her my feelings...(I know I know, I'm an idiot)
Thanks guys.