Had anyone taken a lady to a swingers club?  Should I expect her to find a guy?  What if I find a lady?  What if we find a lady?
What about marks from the prior days BDSM with a Dom, would that be awkward for the “date”?

If she is good looking, guys will find her.  The unknown is whether there will be any women there who are interested in doing you.  This often happens when an average guy shows up with a hot woman.  The solution is to find a girl to take who is the female equivalent of yourself in appearance.  Don't take a girl who is way hotter than you, or you will spend the evening watching HER fuck the line of guys that will form.  

 
It will only be awkward if she doesn't know anything about it until you get there.  

then don't. just don't.  IMHO ...
These places can read confidence, or lack there of, better than any pack of dogs.  
If you are not 100% sure of the LAST thing you'd want to do is take a date.  
PLus you'll likely need ot purchase a membership. Take a weekend, go check out the scene, get comfortable with the layout and the chances of a worry free night of frolic increase 1000%
btw - depending on the city check FL for the best promoter nights and go have a blast!