IMHO, this is a difficult question to answer, because there are so many variables involved. Much depends on what type of bar you want to visit and where it is located. Moreover, what is the attitude of the customers and management toward LGBT people?
Above all, your personal safety is paramount!
For example, I live in the greater Atlanta, Georgia metro area. In general, Atlanta is a LGBT friendly area, and people treat CDs like anyone else. However, the further one travels away from Atlanta, much more traditional thinking prevails, and bars are frequented by some pretty rough people. College town bars are exceptions.
Why even consider a bar? I am a career retired US Navy sailor, and I can say from personal experience that virtually every bar in the world smells of stale beer and cigarettes. Not exactly the odor I want seeping into my pretty clothes.
That being said, I have visited bars with CD girlfriends who want to stop by for a drink. My experience in the Atlanta area? We are treated like any other customer. However, we know beforehand what type of bar we are walking into. Over the years, I can recall very few instances where anything negative was said or done. Loud drunks come to mind. Be aware of them and observe how aggressive their behavior is.
Hey, I guess it all comes down to being aware of your surroundings and exercising common sense.
Oh, one good suggestion. If in doubt, contact management, and ask them if CDs are welcome and will it cause any problems with other customers. I used to do that when I arranged social activities for a group of CDs.
Enjoy being a girl!