You cited John 3:29 as proof text for that teaching. The problem is it simply doesn't say that.
John chapter 3, as you know, is about those who are
born again (3:16). Surely those who receive eternal life through the new birth comprise those added to Christ as His increase. They are therefore the Bride of Christ in every potentiality.
I don't know how. you could possibly say the bride of those following Jesus could not include everyone who is born of the Spirit is principle.
There is a "Bride of Christ", but it isn't "The Body of Christ" that you and I are members of today.
The Bride of Christ HAS to be the Body of Christ. For the Bride must have the divine life of the Husband Christ who regenerates everyone who is born anew. Without having the divine life of Christ we cannot be either of His Body or of His Bride and Wife.
No one NOT possessing the life which is Christ imparted can be a member of either His mystical Body or His Bride and Wife. Having Christ as life is the first qualification to be a member of His Body and a constituent of His Bride and Wife.
The two allegories emphasize two somewhat different angles of the believer's relationship with Christ.
Body of Christ - focuses on a corporate entity with His life enabling Him to move and act upon the earth.
Wife of Christ - focuses on a corporate entity for Christ's satisfaction in love.
Bride of Christ - focuses on the Wife for "one day" so to speak. A wife is a bride for the initial time. IE. on the wedding "day" the long term wife is the bride.
That both the Body and the Bride have to refer to the same corporate entity is proved in Ephesians -
1.) The church is the body -
"Now you [the church in Corinth]
are the Body of Christ, and members individually. And God has placed some in the church, first apostles, second prophets, ... etc. etc." (1 Cor. 12:27,28)
This proves that the Body of Christ is also the church of Christ.
2.) The church is the wife of Christ as well as His Body -
"For a husband is head of the wife as also Christ is Head of the church, He Himself being the Savior of the Body .... Husbands love your wives even as Christ also loved the church and gave Himself up for her " (Eph. 5:23-25)
The church is Christ's Body of which He is the Head and the Savior as well as Christ's wife.
Of course the Bride is the Wife for a shorter period of time initially. IE. a wedding day or what we might consider an initial "honeymoon" period of just coming together.
There should be no argument that Wife and Bride are virtually interchangeable. And there should be no argument that in Ephesians 5 the church of Christ is both Body to Christ and Spouse to Christ.
"In the same way the husbands also ought to love their own wives as their own bodies; he who loves his own wife lives himself, For no one ever hated his own flesh, but nourishes and cherishes it, EVEN AS CHRIST ALSO THE CHURCH, Because we are members of His Body." (vs. 28-30 my emphasis)
I must refer you to this passage to begin.
Rev. 22:9-14
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 had a wall great and high, [and] had twelve gates, and at the gates twelve angels, and names written thereon, which are [the names] of the twelve tribes of the children of Israel:
On the east three gates; on the north three gates; on the south three gates; and on the west three gates.
And the wall of the city had twelve foundations, and in them the names of the twelve apostles of the Lamb.
The "Body of Christ" is just that. The "bride of Christ" is another entity altogether, contrary to the popular teaching.
Ephesians 5 should be plenty enough to prove that the church is both the Body of Christ and the Wife of Christ. I really don't think other proofs are needed.
Now the church, at the end of the millennial kingdom, is enlarged to include ALL the old testament saints of Israel as well. All of God's redeemed people from both the Old Testament dispensation and New Testament dispensation, end up in ONE corporate "city" which is Christ's Bride and Wife in Revelation 21 and 22.
This IS the church. But it is the church enlarged. It is the church increased to include not only New Testament saints but Old Testament saints as well.
So upon walls the names of the twelve apostles of the Lamb to signify the New Testament saints. And upon the gates the names of the twelve tribes of Israel to represent the Old Testament saints.
In eternity future they are all united to be New Jerusalem. And you should not think of the New Jerusalem as being anything other than the increase and enlargement and expansion of the new covenant church.
For length's sake, additional things which need to be also mentioned, will have to wait.