Is it normal that i would have sex with another girl but wouldn't date one?

I've always considered myself straight. I love men. I'm sexually and emotionally attracted to them. But recently I've found that I've been attracted to girls too. The idea of sex with another girl is hot to me. Maybe because it's forbidden, and something new for me. But the idea of being in a relationship with one isn't very appealing. I have no problem with being gay or bisexual, if that's what I am, but I've read that you're only considered gay or bisexual if you're emotionally attracted to a gender, and I'm just not emotionally attracted to other women. As sexy as I find some girls to be, I could never fall in love with them the way I can with a man. Is it normal to feel this way about women?