There are a couple of reasons. First of all, the Director wants to meet Bernard in a public place so that he can publicly humiliate him. Bernard’s actions have been perceived by the Director (not to mentions others) as anti-establishment. He is going against the norms and expectations of the Brave New World, so the Director wants to make a public example of him by shaming him in front of others.
Another reason that the Director chooses the Fertilizing Room is because this place has been the source of rumors surrounding Bernard. Many believe that alcohol was put into his blood surrogate, explaining his height and his odd behavior. What better place to humiliate him? But remember, it was Huxley that chose this location, as it serves to further the plot. Linda’s entrance in this public place, the place where the Director is respected and feared to some extent, is the perfect place to turn the tables and to ensure the Director’s complete and total humiliation. Not only is it ironic, but it is pretty scandalous and entertaining as well.