To say that an ecclesial body is in partial, or imperfect, communion with the Catholic Church is not to say that the members of these bodies are only partially "members of the body of Christ":
[People] who believe in Christ and have been truly baptized are in communion with the Catholic Church even though this communion is imperfect. The differences that exist in varying degrees between them and the Catholic Church—whether in doctrine and sometimes in discipline, or concerning the structure of the Church—do indeed create many obstacles, sometimes serious ones, to full ecclesiastical communion. The ecumenical movement is striving to overcome these obstacles. But even in spite of them it remains true that all who have been justified by faith in Baptism are members of Christ's body, and have a right to be called Christian, and so are correctly accepted as brothers by the children of the Catholic Church.
(Unitatis Redintegratio, Chapter 1, Section 3; emphasis added)
Referral to "partial/imperfect communion" is thus referring not to "communion with Christ" but rather to "communion with the structure of the Catholic Church". What is it then that these people are missing?
Our separated brethren, whether considered as individuals or as Communities and Churches, are not blessed with that unity which Jesus Christ wished to bestow on all those who through Him were born again into one body, and with Him quickened to newness of life—that unity which the Holy Scriptures and the ancient Tradition of the Church proclaim. For it is only through Christ's Catholic Church, which is "the all-embracing means of salvation," that they can benefit fully from the means of salvation. We believe that Our Lord entrusted all the blessings of the New Covenant to the apostolic college alone, of which Peter is the head, in order to establish the one Body of Christ on earth to which all should be fully incorporated who belong in any way to the people of God.
In other words, those who are baptized (with the same intent in, and understanding of, Baptism that the Church has) but are in another faith community are missing opportunities to believe in and to practice things which could be conducive to their salvation.
There can be no biblical basis for this "belief" (which is really not so much a belief as a standard of speech), since the fracture of the Church into these communities did not take place until well after biblical times.