I was unable to find your quote in the most likely place, the introductory chapter, but I may have missed it, or it may be from the newer edition. But it’s important to realize that the context of Bauckham’s “Mission Statement” is “The Quest for the Historical Jesus,” which is a small and highly specialized field, with its own traditions and methodologies, and that is the “recent scholarship” that he is critiquing, not the whole of New Testament studies. Indeed, it organised itself as an authoritative body (“The Jesus Seminar”), complete with a deliberate consensus-forming voting system, communicate a particular position to the public.
In particular, Bauckham examines the assumptions of the “form criticism” which, although it is largely abandoned, have continued to influence this particular genus of historian:
Although the methods of form criticism are no longer at the center of the way that most scholars approach the issue of the historical Jesus, it has bequeathed one enormously influential legacy. This is the assumption [my italics] that the tradition about Jesus, his acts and his words, passed through a long period of oral tradition in the early Christian communities and reached the writers of the Gospels only at a late stage of this process.
This is despite the consensus that developed after form criticism that the gospels were completed within living memory of the events (60-100 CE). Richard quotes the scholar most responsible for introducing German form criticism into English scholarship to show the problem with this:
If the Form-Critics are right, the disciples must have been translated to heaven immediately after the Resurrection.
In other words, if the gospels don’t embody eye-witness, why not? He further explains the methodological bias that this has given to the rather small “historical Jesus” community:
It is essential to realize that this is not just treating the Gospels as historical evidence. It is the application of a methodological skepticism that must test every aspect of the evidence so that what the historian establishes is not believable because the Gospels tell us it is, but because the historian has independently verified it. The result of such work is inevitably not one historical Jesus, but many.
As Kuhn demonstrated so well for science, any field of study develops its own traditions and biases that are not easily shaken (think of the adaptationist wars). So one can’t enlist a “consensus” to one’s cause without careful consideration of the human reasons, from what is taught in the introductory textbooks to “groupthink,” for the existence of that consensus.
One such mechanism, all too evident nowadays, is who gets to say what is the consensus, and be quoted in secondary sources like Wikipedia. In this case the “consensus,” in fact, does not mean agreement on the goal of the discipline (“Who was the historical Jesus”) but merely the methodological assumptions, which are not evidence.
Finally (in addressing that question of what “most scholars” think), I have a relative who is a modern Russian historian, who in her career during the cold-war was an outlier in her field for being skeptical of the Soviet system. The reason she was in a minority? Most colleagues only entered the field because they admired communism. Now, after the collapse of the Soviet System, she is mainstream, which is why her book on Lenin is still in print, and theirs aren’t. The prevalent assumptions of her discipline were, it turned out, ideological rather than evidential.