Hi there,
Cuckold husband here, but I can share some of our experiences as a cuckold couple.
Short version is we started out always playing together, and now it's a 50/50 mix of her going out on her own and me being present in the room, though she won't do any overnights. And it only takes her one date with a Bull to know if she would see him alone or not. She has told me its mostly about chemistry, the stronger the chemistry is the more likely she'll want to be with him alone.
Long version...
My wife and I have been in the lifestyle for about four years now, though hampered by the pandemic, we have generally averaged seeing a Bull (either new or regular) once every few months.
For the first three years, my wife and I always played together. I was always there or in the same vicinity, if not exactly there. For example, sometimes I would be sent to the guest bedroom and she and her Bull would take over the Master bedroom.
This last year, we began to explore her meeting up with Bulls completely alone. First it started with dirty talk between her and I, and then more longer conversations exploring the details of how it could work, until one day we decided to try it with one of her regular Bulls.
I booked a hotel, took her to the hotel, checked in, and escorted her to the room. Watched her put on some sexy lingerie, before she told me she got a text from him that he was parking and I should be going.
I didn't hear from them until he sent me a text hours later that night. It was a picture of her, on her back on the bed, his cum dripping out of her. He didn't say much, just that he was "done with her" and that I should "come get your women".
That night went really well, for both of us. I really enjoyed the humiliation of not being allowed to be there, and she liked being able to focus her attention on her Bull and worrying less about me.
Since that night, we've averaged about a 50 / 50 split of play dates where she either meets her Bull alone, or where I'm in the room or nearby.
She has never mentioned anything about having a preference (at least not to me), and has said she enjoys aspects of both.
Hope that's helpful in some way.