Interesting and some good answers so far. ImO a couple just is in the position to be selective. For them an additional guy or lady is a plus, not a necessity - they already have each other on a regular basis.
But in the end the choice is made by all involved parties. A lover or "bull" may not be available for some couples as well, when the chemistry just isn`t there or ideas are not compatible.
As for the question "who`s more dominant or has more say, the wife/gf or the husband/bf?" - That depends on the couple; everytwo are different in this.
For hotwifing couples who seek a male partner for the wife/gf it seems obvious that the woman takes a great part in making the decision, as she will be the one to enjoy the other man.
In many cases it will be the husband/bf though who does first filtering in place of his woman. An advantage of this approach is that the husband/bf doesn`t give up all control over the situation which is comforting for himself but also for his woman as, by doing so, he actively shows his approval. Also that turns it more into a "couple thing" and further away from the characteristics of cheating.