Not the Church itself, but the City Where God's Saints will Dwell
The Book of Revelation adopts the metaphor of the prophet Jeremiah, who spoke of Jerusalem as God's bride.
Jeremiah 2:2
Go, cry out this message for Jerusalem to hear! I remember the
devotion of your youth, how you loved me as a bride, Following me in
the wilderness, in a land unsown.
Thus, in Revelation 21:2 we read:
I also saw the holy city, a new Jerusalem, coming down out of heaven
from God, prepared as a bride adorned for her husband.
Jerusalem was not synonymous with the people of Israel was their holy city. Thus, the bride is the restored holy city, not the congregation of saints. This becomes even more plain when we read more of chapter 21:
“Come here. I will show you the bride, the wife of the Lamb.” 10 He
took me in spirit to a great, high mountain and showed me the holy
city Jerusalem coming down out of heaven from God. 11 It gleamed with
the splendor of God. Its radiance was like that of a precious stone,
like jasper, clear as crystal. 12 It had a massive, high wall, with
twelve gates where twelve angels were stationed and on which names
were inscribed, [the names] of the twelve tribes of the Israelites. 13
There were three gates facing east, three north, three south, and
three west. 14 The wall of the city had twelve courses of stones as
its foundation, on which were inscribed the twelve names of the twelve
apostles of the Lamb.
This is a place - whether on earth or in the spiritual realm - where the saints enter and dwell. It is not the congregation of the saints (the church) but the place God has prepared for them to occupy. Thus we are told:
The nations will walk by its light, and to it the kings of the earth
will bring their treasure. 25 During the day its gates will never be
shut, and there will be no night there... (chapter 22) The throne of
God and of the Lamb will be in it, and his servants will worship him.
As to who are the people invited, they are those who have passed through the trials described in the previous chapters, leading up the fall of Babylon in 17-18.
Conclusion: In the Book of Revelation, the "bride" is the new Jerusalem. Because Revelation is open to so many interpretations, I will not go further in order to avoid theological speculation. However, the text makes it clear that the bride is the new Jerusalem and those invited are those who have gone through what has been described in earlier chapters. As long was one distinguishes between the new Jerusalem and those invited, the problem presented by the OP is resolved. The "bride" is the city; those invited to the wedding are those who will enter it (Rev. 21:7).