Hey there, welcome.
I have to second some of the stuff that was said already. Biggest possible issue: don try to MAKE her feel anything. Her emotions are her own, you shouldn't meddle and try to manipulate her into something. Be fair, let her come to a conclusion on her own. When I confronted the ones I loved with my wishes and thoughts, of course I wanted them to consider them as possible and OK and was afraid of them saying "Never, ever!" but that's just what can happen. You can't make someone feel something.
What you can do, is taking baby steps to reach a place where she will be able to understand what you are talking about. The smaller the steps the better the processing. Talking about it in a more theoretical context has helped some of my friends to wrap their mind around it. For example, I told a friend about 'some friends' who happen to find themselves in a vee eventually and they have been happy for years now. On that basis I talked about what was on my mind concerning my two partners. When I later (some months) told her the truth about my relationship(s), the light bulb moment came instantly when I mentioned it because of the story we talked about before. So, if she never heard of it, she may need some time to think about the whole range of possibilities without feeling pressed or threatened to reach a certain comfortable place as quickly as possible because the matter stands right in front of her door already. If you have the chance ease her into it.
When I confronted my husband with the whole mess, he was surprisingly OK with it. He needed some time still, but he was OK. This isn't the way it normally works (as far as I can evaluate it). You are turning her world upside down by going beyond the standards she knows and feels comfortable with. Even in the case of my husband he lost trust in our relationship first. Don't expect her to be happy and suddenly 'discover' a side of her that has always been there. This may happen, but it could go in a totally different direction. And as she hasn't expressed a clear attraction to your mutual friend, (the things you described are just everyday stuff and perfectly normal) her reaction is more likely to be not that positive in the beginning.
Wishing you luck on your path, Phy.
Facts: 30, female, bi, v-type relationship with Sward (husband, straight, mono) and Lin (boyfriend, straight, mono), poly-fi and co-primary.