Who is the Bride of the Lamb?
The Bride of the Lamb is the Church, the redeemed of Christ, who are pictured as His wife arrayed in fine linen and also shown as the holy city, New Jerusalem.
Revelation speaks of the Bride of the Lamb as the Church, the company of the redeemed who belong to Jesus Christ. At the Marriage Supper of the Lamb, the wife is described as having made herself ready and being arrayed in fine linen, clean and white, and this fine linen is said to be the righteousness of saints. This shows that the Bride is made up of those who remained faithful and prepared for Christ's coming, now purified and glorified, entering into everlasting communion with Him.
One of the angels who had the seven vials says to John, Come hither, I will shew thee the bride, the Lamb's wife, and then carries him away to see that great city, the holy Jerusalem, descending out of heaven from God. Because the husband and the bride are one, the city itself is identified as the Bride of Christ, the visible form given to the union between the Lamb and His people.
So the Bride is not a separate group from the Church; she is the Church herself, the redeemed who are called unto the marriage supper of the Lamb, clothed in righteousness, and joined to Christ in eternal fellowship as He prepares to reign with her in glory.
The scriptures
And I heard as it were the voice of a great multitude, and as the voice of many waters, and as the voice of mighty thunderings, saying, Alleluia: for the Lord God omnipotent reigneth. Let us be glad and rejoice, and give honour to him: for the marriage of the Lamb is come, and his wife hath made herself ready. And to her was granted that she should be arrayed in fine linen, clean and white: for the fine linen is the righteousness of saints. And he saith unto me, Write, Blessed are they which are called unto the marriage supper of the Lamb. And he saith unto me, These are the true sayings of God.
And there came unto me one of the seven angels which had the seven vials full of the seven last plagues, and talked with me, saying, Come hither, I will shew thee the bride, the Lamb’s wife. And he carried me away in the spirit to a great and high mountain, and shewed me that great city, the holy Jerusalem, descending out of heaven from God, Having the glory of God: and her light was like unto a stone most precious, even like a jasper stone, clear as crystal;
And I John saw the holy city, new Jerusalem, coming down from God out of heaven, prepared as a bride adorned for her husband.
From the books
This answer is drawn from these passages in the Mary Banks Faith Library.