Further to this whole connection between the images of the body and the bride, consider the way Ephesians 5:26-33 frames the issue:
Husbands, love your wives, just as Christ loved the church and gave himself up for her, in order to make her holy by cleansing her with the washing of water by the word, so as to present the church to himself in splendor, without a spot or wrinkle or anything of the kind—yes, so that she may be holy and without blemish. In the same way, husbands should love their wives as they do their own bodies. He who loves his wife loves himself. For no one ever hates his own body, but he nourishes and tenderly cares for it, just as Christ does for the church, because we are members of his body. “For this reason a man will leave his father and mother and be joined to his wife, and the two will become one flesh.” This is a great mystery, and I am applying it to Christ and the church. Each of you, however, should love his wife as himself, and a wife should respect her husband.
Here the image is, thoroughly relational, centered on the union between two spouses. It is precisely in that context that the image of the church as Christ’s body is referenced. The church here is seen as Christ’s body in the sense that Christ loves it as he loves himself, with the very love that God is. Thus the church is the body (at least here), not in the sense that it is mystically the same person as Christ, but that in Christ’s love it is brought into the deepest possible intimacy in relation to him.
Christ regards the church as his body precisely as the bride. Both images speak, seamlessly, of the infinite love that Christ has for the church, that he lavishly bestows on her, loving her so as to give himself way for her sake.
Thus the image of the “one flesh” — which describes the intimacy, both conjugal and social — of a husband and wife serve to illuminate the image the church as Christ’s body. The church is the “body” of Christ precisely in the sense that spouses’ bodies belong to each other. The church is Christ’s body because he has utterly and radically given himself to her in love, to which the church responds in gratitude, love, and service.