Only to the bedroom, but not on "dates". It should be sex only.
Obviously I may well listen or watch sometimes but if they occasionally do it when I'm not there, that's generally fine.
However, in my previous open relationships and cuckold relationships the girl usually had multiple fuck friends (or bulls as they are called here), making it less likely that she would develop an emotional connection.
I think if you spend a lot of time with any one person, feelings can happen; which is why it's arguably better that she has multiple options when she is horny.