Club Silencio is not a transition scene between the two main parts — dream and reality. It is the third. The final one.
The story starts when Diane wakes up. Camilla comes around and tells her their affair's over; they have a fight. When Diane realises — after the dinner party — that Camilla won't come back to her, she hires a hitman to kill her. She's jealous, she's crazy, she feels remorse. She shoots herself.
Then the Cowboy enters and says: it's time to wake up, baby. You have another chance, another try.
And we see her going down the escalator at the airport. Now she's Betty. She meets Rita. Betty suddenly remembers that she loved her — she loved Camilla when she was Diane. When they come home from Club Silencio, Betty disappears. Rita whispers "¿Dónde estás?" — "Where are you?" — and opens the mysterious blue box. And then it all ends.
It's over. The dream is over. Another chance, another try turned out to be a dream. And it ends. Silencio.