Item number one: there really is NOT any "private" room in Baby Dolls, Dallas. What you can rent, for an excessive price, is one of those booths along the walls - no real privacy. In BDs your best option for increased fun is find a lady who will take you behind the stage and build a chair fort during the day shift.
Also available near to BDs is the Cabaret Royal (6 or 8 blocks away) where the room is darker and chair forts are common. the CR also has an upstairs (not much more privacy) and semi private rooms (also overpriced). Adjacent (and attached) to the CR is the Faire Room (an all nude, BYOB, juice bar. The Faire has been raided a few times and recently the action has been hit or miss. One nice option is you can get a "VIP" admission to the Faire and go back and forth between CR and Faire with no additional charges (daytime price $30, but it goes way up if you buy it later in the evening). If you bring booze, the Faire staff will hold your bottles for you when you got to the CR.
Just down Mananna St is the Clubhouse, another nude, BYOB club, The Clubhouse has a Rock and roll theme (it is owned by an aging rocker). It has a ground floor VIP with little privacy but at least it is separated from the open main floor. The club also has a $35 "VIP" upstairs which is also pretty open but covers a lot of space and is seldom crowded, so privacy can usually be found.
Fun can be found at all four clubs, but remember it is up to the girl what is on the menu. My experience is that day shift, middle of the afternoon, is the best time to find ladies looking to earn a little extra for fun (except the Faire Room - days are usually dead there).
Good luck and good hunting.