What you can do is simple: leave it alone. At least for now. She has made her feelings clear in not wanting to have a threesome and it is her choice and what she wants or does not want, not what you want.
My wife and I were once involved in swinging which included both men (and women) having sex with her and myself with other women. Any session was talked about prior and agreed upon and if one of us didn't feel comfortable with a certain act, situation or the other being with a certain person, we respected it and didn't do it.
During that time, I've seen and heard about too many couples that tried to force the issue because only one was into the fantasy and overeager (almost always the man) and it always resulted in disaster, sometimes even dissolution of the relationship. I personally witnessed a freakout from a woman during a group session and it became very clear afterwards that her husband had pressured her to attend the event even though she was not comfortable with it.
So, the way I see it there really is no dilemma because your only choices are to either respect her feelings on the matter and drop it or push the issue and risk your relationship. Since I'm assuming you care about this woman and want to continue to be with her and maybe have the relationship grow, option one should be the only consideration.
The only other suggestion I would recommend would be if it is really something you want to experience, wait a time, maybe a few years, and float the idea again once you two have more history together under your belts. While you haven't said how long you two have been together, I can tell you my wife and I both would have turned down swinging early on in our relationship if the other had brought it up. It took almost 15 years of marriage before either one of us were comfortable considering having sex with someone else and willing to admit it was a desire and pushing the issue before that timeline would have been detrimental and we probably would be in a different place marriage-wise today.
Watch some porn together, roleplay or discuss fantasies in non-committal terms, but otherwise do not pressure her or appear overeager and make it all about you. It is her body and her choice whom she shares it with.