If the days of Reimarus to Schweitzer were the old quest, the period of Bultmann is the “no” quest.Dale Allison argues in "The Secularizing of the Historical Jesus" (which used to be available online, and which you can still grab from the archive.org if you don't have access to his recent book in which it appears) that the period of "no quest" or "non quest" is a phantom, and I think he makes his case effectively. As Allison points out, many books about the historical Jesus were produced during that period, e.g. most famously by Joachim Jeremias. The idea of a "no quest" really only comes from a particular reading of Bultmann's students' supposed relaunching of the quest in the 1950s and 1960s.
While on the topic, it is worth pointing out that one can read some Bultmann online; I've lifted the following from the relevant lists on the New Testament Gateway:
Rudolf Bultmann & Five Critics, Kerygma and Myth
Full version from Religion On-Line of the English edition of a famous book featuring Bultmann's essay "New Testament and Mythology", answers by five critics (Julius Schniewind, Ernst Lohmeyer, Helmut Thielicke, Friedrich K. Schumann & Austin Farrer) and Bultmann's responses.
Rudolf Bultmann, Jesus and the Word
Full reproduction of the English translation of Bultmann's classic book of 1926, prepared for Religion On-Line by Ted & Winnie Brock.