As was Said in the Last Sentence, The Bride has Arrived.
The words of the song say that the bride wore only white on her wedding day. In this case, a female comedian has made fun of the idea of mail-order brides. Even so, it is very unlikely that her joke went something like, “Here comes the bride, delivered by the postman in a box.”
She acted out the part in “The Wedding Singer” where the bride is given to the groom as a package. In this scene, the bride is shown to the man she is going to marry. At this point in the story, the bride is given to the groom. The level of cynicism that this group always shows never stops making us laugh.