If it were me at 19 (with a guy my age, lol), I would go out with him. But: I've been on dates, had relationships, had the first kiss, etc. When you're younger and haven't had the first relationship, it's a lot more of a big deal. Now that I've been through all that, I can go out with someone and if I don't like them, just accept it and not pretend like I do. I don't feel obligated to please him or anything. I can simply tell them that and try to have a good time.
If it were me at 13: I would probably be feeling very similar to you right now, lol. My first date was at 14 with someone I wasn't crazy about, but I went out with him because I thought the person I really did like would never ask me out. I even had the bi feelings like you do now. I really wanted boys to like me at that age and made bad decisions.
I say think about it a little more. He wanted it to be just you two, but why not hang out in a group? That puts less pressure on you and it's usually more fun anyway. On a side note: I wouldn't open up to him about the bi thing unless you're open about it to everyone.