'The Bachelorette' Stars Andi Dorfman & Josh Murray -- First Public Outing After the Finale (VIDEO)

With the finale of "The Bachelorette" having aired Monday night, Andi Dorfman and her new fiancé Josh Murray can finally go out in public together ... and they did so the first chance they got.

Dorfman picked Murray over fellow suitor Nick Viall and the new couple immediately jumped on the red eye at LAX to do the morning shows in New York City.

Andi and Josh clearly couldn't wait to be together -- the video was shot around 9:15 PM PT ... and Dorfman making her pick didn't air on the west coast until around 9:45 PM.