When you're in a monogamous relationship and you start wanting to bang other people you can either change the rules, repress it or break up. (unless you're a disgusting human being then there's a 4th "hidden" option)

You said she doesn't want an open relationship, so changing the rules is not an option. I wouldn't be pushy about this, opening a relationship has to be a mutual interest otherwise it will result in disaster.

You don't seem to want to repress it either. It's a newfound attraction, you say it's intense and you want to experiment with it.

So... that means you should probably break up with her. You guys don't really seem to be compatible at all, you want a guy and she wants a monogamous relationship with a girl. You could try some palliatives like strap-ons but something tells me you wouldn't be satisfied by just that. Considering how many ways this could go terribly wrong, breaking up with her is a very healthy way to end the relationship.

just don't go for the 4th option OP, don't do that to your gf