I definitely am not gonna just ask her out because to me that seems even more shady then just hanging out and hooking up...
what a half-assed personal boundary... pffft. \
Anyway, she's in a relationship with a man wherein they have both agreed that sex outside of the union is acceptable to both of them. You are the third wheel here. I suggest you just bang her and then get out without any bonding rituals because you're likely to be the one that is going to end up chasing and chasing her until YOU fall in love when she loves someone else. I say that because if you were the casual sex type that could actually just handle this for what it is, there would be no need for you to run it by a forum full of strangers before you started humping away. No "hanging out." Just keep it to "hooking up."
“The willingness to accept responsibility for one’s own life is the source from which self-respect springs.” ~Joan Didion