We never see Rory ask Dean to be her escort for the ball, but we can safely assume he agreed with the greatest reluctance, because the first time we see him in this episode, he seems bewildered, dismayed and rather sulky as he discovers just what escorting Rory to her debut entails.
In real life, it is not recommended debutantes ask their boyfriends to be their escorts. Not only would a break-up put everything in jeopardy, but relationship dramas can create an unwelcome distraction. Some debutante committees even ban them outright, and it’s common for the committee to pair girls up with a suitable escort of their choosing – usually a boy or young man who has experience of cotillions and debutante balls. The DAR would have probably chosen someone rather like Tristan to be Rory’s escort (which could have been an interesting take on the episode).
As Rory is a very late entry, perhaps she has organised her own escort, along with her own dancing lessons and so on.