I think you might be comparing the console version to the PC version. Even when you complete the game you don't get the option to play her individual missions. You can switch to her in free-play once you completed the game though. When I pre-ordered BM:AC, catwoman came as a pre-order bonus. I don't remember seeing an individual icon of catwoman on the menu since I had it but it was on the console versions of the game.
Well I don't think I confuse anything due to I had it before the GFWL removal patch...
Just to clarify this, as I've had the same issue. The Catwoman storyline / option only appears once you have a Steamworks save file or a played up until the point that you can play Catwoman for the first time.
The conversion of a GFWL save to Steamworks for some reason does not activate the Catwoman option.