The oath starts at around 3:08. After the oath is completed, Biden says:

Justice, these are some of my friends, my family. I want to explain to you what a wonderful honor it was and how much our of her way the Justice had to go. She is due in New York. She has to leave right now. I apologize. We have to walk out. Her car is waiting. She has to catch a train I hope I didn’t cause her to miss . . . Madam Justice, it’s been an honor.

And then Sotomayor exits immediately while Biden walked around shaking hands. I still think this is inappropriate. At least someone is riding Amtrak.