I'm glad that you were able to move past your previous jealousy issues and be-friend this girl. In all honesty I think it wouldn't be a very good idea for the two of you to "go out" or "hang out" with this girl for the simple fact that you'll see how well they get along, how friendly they are, ect.
I must say that if you still haven't fully over-came these issues that have tormented you and your relationship in the past then be-friending this girl could be very destructive. If in fact these issues still remain seeing your fiance and his one night stand together being friendly, chatting, laughing, physically interacting, ect may bring about thoughts/doubts on how friendly they really are when you're not there. How well their work relationship "really" is....ect. It may cause you to doubt him and un-ravel all the work you've done as far as over-coming, forgiving him, ect.
Evaluate how you really feel about this then go from there and decide if in fact you really want to be friends with her or if keeping your space would be the best option for you and your relationship.

Good luck!