Is there some sense in which Christ is the head of one body of Christ, the church or is Christ somehow the head of many bodies of Christ and the head of many local congregations?
Christ is the head of all churches. Or at least he should be.
In most uses of the word "church" in the New Testament, most of the time it is used in conjunction with a place name. "The church at Corinth." "The church at Ephesus." Etc. All obviously referring to local churchs.
In many other places the word "church" is used in the plural, (Acts 15:41 and 36 other instances). All obviously referring to local churches.
The third usage is that which you have referenced above. The word "church" is used generically. "No church specifically, all churches in general."
This is a fairly common use of language. "I believe the horse is the most beautiful animal in God's creation." When I use the singular "horse" it means "all horses in general, no horse in particular." It does not mean, of course, that I believe in a "universal, invisible horse."
I believe the dog is the most loyal of all of God's creatures. Because I use the word "dog" in the singular does not mean I believe in a "universal invisible dog." It means I am using the term in a general rather than specific way.
As to the the "Bs" - the body, the building, and the bride.
One of the very first things I learned in seminary was to not make a passage "walk on all fours." Read it to understand the author's intent.
Body, building, and bride are all metaphors used to teach church truth.
One of the great methodologies of pedagogy is to use what the people are familiar with to illustrate a new truth.
Everyone one is familiar with a body. We all have one!
Everybody is familiar with a building. We have all been in one.
Everybody is familiar with a bride. We either have one, or we are the son of one.
So God's word uses that which we are familiar with to teach us new truth.
The body is used to illustrate service through our church. Hands to reach out with, feet to carry us to where we ought to be, a mouth to preach the gospel.
The building is used to illustrate the church as being the shelter from the storms of life, and, especially to the Jews, the house of God where we can come and bring our needs to Him and our offerings to Him.
The bride is used to illustrate the faithfulness of the church. The love relationship. This term is contrasted in Revelation with the "harlot" - speaking of a lack of faithfulness.
Don't make the 3 Bs walk on all fours. Understand them as the teaching metaphors they are.
