Why don't they play, "Here comes the bride" at a Jewish wedding?

Answer:

We have our own beautiful Jewish songs to sing at Jewish weddings. At such an important milestone in life we wish to emphasize that it is a Jewish milestone in a Jewish life, and so it is no wonder that we choose Jewish songs for this event.

Furthermore, the traditional Jewish songs are not just nice melodies, but blessings as well.

When the bride and groom come under the Chupah canopy a cantor sings the following song (usually in Hebrew):

”Blessed are those who are coming. He Who is the Al-mighty and Omnipotent, over all; He Who is blessed over all; He Who is the greatest of all; He Who is distinguished of all; He shall bless the groom and the bride.”