The Bridegroom here is Christ, because he espoused the human nature, and, through it, the Church to himself in his holy incarnation. This holy union he began by his grace on earth, and he will consummate it gloriously with his elect in heaven, when "the marriage of the Lamb shall have come, and his wife shall have made herself ready."
Hence John the Baptist calls himself the friend of the Bridegroom, that is, of Christ. The sons ( υἱοὶ) of the bridechamber are the special friends of the Bridegroom, those who are admitted into the closest fellowship with him.
The expression is a Hebraism, like "the children of disobedience," and many other similar forms of expression. So long, then, as the bridegroom is with them they cannot fast. But the days will come when the bridegroom shall be taken away from them, and then shall they fast.
It is as though our Lord said, "It is not surprising that they should not care to fast as long as they enjoy my presence; but when I am taken from thegn, then shall they fast."