The only way to miss church membership in the Bible is to ignore the Old Testament or to mistakenly think the church did not exist yet in those times. The assembly of God's people is carefully counted and individuals listed by name in Numbers 1-4 and 26, and in Ezra 2. That's six whole chapters of Scripture dedicated to the practice of numbered, named church membership. Would one of the slaves freed from Egypt tell Moses he wanted to tag along to the promised land but did not want to be named and registered as a part of the congregation, as mentioned in Numbers 1:18? Or would one of the returnees from exile tell Zerubbabel he wanted to come with him to Jerusalem, but to please not list him among those catalogued in Ezra 2?
As we move into the New Testament, I would think the burden would be on the one opposed to membership to show that God no longer cares about numbering his people, and that belonging to the assembly is now more of a fuzzy free-for-all. This would be hard to show in light of ample evidence that God does still care who belongs and wants the leaders of his church to know whom they are overseeing, just like Moses and Zerubbabel did. Acts 2:41, Acts 4:4, and Acts 6:1-7 show that the church kept tracking its numbers and membership into the apostolic age, and passages that speak of expelling members (like 1 Corinthians 5:2) imply the church leadership knew who was in to begin with. You can't expel him if he's just looking in from the fringe, can you?
Of course, in the apostolic age, baptism would have been enough to show church membership and get you numbered. If you were baptized you were part of the body, and everyone knew which local church you belonged to since there weren't multiple choices in each city. In that sense, what we refer to as church membership today is a bit different in that it also helps us specify exactly which elders in what local church are in charge of a member's care. But it is a mistake to claim that to have some membership in some church is nowhere taught in the Bible. It's very clearly there.