Being the 'third' in my relationship, I know my girlfriend had the same problems it seems you are probably going to. But what happened for us was that I met Arris in an online writing community - not really planning on getting involved or having our relationship go the way it did. We were friends for about a year beforehand and got to meet in person around that time. Things just kind of sparked from there.
Arris has always been in a kinda...different relationship with her fiancee. They're pretty open people, give each other a lot of space, but definitely had never broached the topic of poly. Which is basically what she had to do once the two of us realized we were really interested in starting a relationship.
It started off very slow, kinda of a bringing up of topic of how she'd like to kiss another girl, or was interested in exploring something there. He automatically said 'no not comfortable with that' - which when you're in a mono relationship for four years...it kind of makes sense. But she's kind of a stubborn girl, and over the months slowly kept bringing it up.
We use the phrase - baby steps - as we've gone through it. And eventually I was brought up. I'd met him before so it wasn't as if I was a complete stranger, and more recently we've been hanging out at different events as a group. So his answer has gone from - 'no way' to 'yeah I'm okay with it'. But it takes a lot of openness and a lot of trust for the kind of relationship we're trying to build. And a lot of time.
Though I'm not sexually attracted to her fiancee (as I'm gay) I've found that being friends with him has really helped to open everyone up to the idea. You sort of have to prove in a way that the new relationship won't come in-between the old one, and can actually enhance what you already have.
Knowing Arris, it's a bit of juggling at times, but we're all very happy so far with the results.