A lot of your concerns and fears are the same thing that I feel and go through. Though I'm not the one that first mentioned polyamory. My husband is also bi and I am straight. I know when we first dated I always told him that he was more than welcomed to have a boyfriend because I was not something I could give him. Though he never took me up on it he has always been completely devoted to me.
I'm not totally closed down to the idea of being poly though I think that your primary relationship must be strong before you could venture off outside that. Our discussions have mostly ended as we think when we are ready another couple would probably be the best for us.
Being how you are bi would you consider a girlfriend for the both of you? Not just his or yours but one girl for the both of you? As in anything communication and respect must there and remember that you and your fiance are the primary.