I'm a secondary in a vee relationship. My partner has been married to his wife for 20 years. He and I have been together for almost six of them. I know his wife; we have socialized a bit but not a lot--she doesn't have much interest in being my friend, and I'm mostly okay with that. I'm not bi, and I have other friends.
But. If you care about your girlfriend, I recommend giving some serious thought to what kind of experience you are creating for her or any other secondary or tertiary relationship that comes along.
I understand that my partner made a lifetime commitment to his wife long before I entered the scene. That means they live together, have a business together, and their finances are intertwined. It means that if she wants to move across the country and he is interested, they will do so, even if it means putting many miles between him and me. Their life comes before our relationship. I'm not always thrilled with that, but I understand it.
That said, I don't feel that he loves her "more" than he loves me. He loves me differently. He does not have the same level of commitment to me, but we have a serious, deeply romantic relationship in which sex is only a part (and a very joyful part, I might add). If she were in trouble, or needed his help, or was struggling in some significant way, he really might call me and try to reschedule a get-together (but I know that I would be consulted, if only as a courtesy). There have also been, rarely, a couple of times when she and I have BOTH been emotionally struggling (over completely different issues), and he has had to make triage decisions--who needs him more right that moment? Sometimes, that has meant being with me.
It's hard enough to be a secondary knowing the primary spouse has veto power over my relationship with her husband. I would have a really really hard time with it if she were feeling like he had to drop everything (including me) any time she snapped her fingers, just to prove she could. Thankfully she doesn't, and is actually very supportive of her husband's relationship with me.
Part of it is because she loves her alone time. And part of it is that she knows I bring things into his life from which she benefits--new interests, renewed passions, lively discussion. She has also told me that sometimes it's a relief knowing there's someone else on board to support him. (She's much more of an introvert than he is or I am, and so she can feel overwhelmed by his energy--whereas I'm really happy to soak it up.)
There's a good "secondary's manifesto" or something like that out there on the Internet. Maybe somebody here knows what it's called and where to find it. I recommend reading it just to get the perspective of what you're asking of your girlfriend.
If you care about her--and the security of your marriage--it has really good questions to ponder.