Open relationships definitely do NOT need to be just one-night stands! FB, in this case, doesn't mean facebook. It means FWB, or Friends With Benefits, which is perfectly normal. Just because someone wants to have sex without being in love doesn't mean they necessarily want sex with a stranger who they will never see again. There's a lot of gray area in between those two extremes.
For myself, I don't usually have a physical relationship with someone unless I like and respect them and they like and respect me. I also don't use the "FWB" label to mean "booty call": we are friends first, the physical part is secondary, usually just for fun. My husband and I were open(-ish) for years before I developed feelings for one of my FWB's and we developed a committed romantic relationship.
I would have an issue with her disappearances- open relationships don't usually work unless every is actually OPEN, being upfront and honest about everything. Which also means being honest if you're not okay with the arrangement. Just because her desire is normal doesn't mean it's automatically going to work for you.
Pan Female, Hinge in a V between my mono (straight) husband, Monochrome and my poly (pan) partner, ThatGuyInBlack