The earlier of two published analyses by Schenker is in an issue of
Der Tonwille—see references at the bottom of this post. It is the only reading with a rising line in his published work.

A facsimile of the detailed reading is below. This comes from my own copy, given to me by my former Indiana colleague Vernon Kliewer on the occasion of his retirement. You can find a cleaner version in Drabkin and Annibaldi, page 63 (again, see references at the end of this post). I wrote this in my JMT article: Schenker "gives an analysis of the first of J. S. Bach’s Twelve Little Preludes in which the essential motion is the 'composing-out of the space of the fourth from G to C.' He describes this motion as accomplished by ^5-^6-^7-^8 over I, followed by a repetition of ^7-^8 over V and I, respectively. . . . By the standards of the fully developed theory, this analysis is unconvincing, but it is more to the point that Schenker’s essay contains no comment suggesting that the rising Urlinie is in any way problematic. In fact one of his closing comments is, 'After this presentation, who can still doubt that this Prelude, through Urlinie, voice leading, and harmony, develops only the triad, the chord of C?'” (276-77; see note at bottom of this post] I then recount how he changed his mind about rising lines over the course of the next two years. As we will see below, I came up with quite a different reading myself—Urlinie from ^5—but on revisiting the matter over this past week, I find this first reading of the piece the most convincing of them all. It charts the course of the upper voice beautifully and therefore also matches the bass and its implied (partimento) figures.



William Drabkin has an equally interesting reading that retains Schenker's upper-voice shapes but expands on them using my three-part
Ursatz device (from another 1987 article). His graph is the lower system below. In the upper system, I have pulled out a pair of unfoldings as a complementary way to relate the two upper voices.
Schenker's later analysis (here in a version from Meeùs, Figure 8) runs from the initial ^3 and shifts a great deal of the earlier-level motion to the pedal-point dominant. Allen Forte and the Forte & Gilbert textbook follow this.
Nicolas Meeùs tries to solve the problem of too much attention to the end by creating a different kind of rising inner voice (the one he labels "Cantizans").
I have an unpublished analysis, probably from the 1980s, in which I read the Prelude from ^5. My octave couplings -- at (a) -- imitate those of the
WTC I C Major Prelude. At (b) sixths elaborate from above, starting from a unique C6 cover tone. At (c) I might have unfolded a third from B4 to the open note D5.
References:
Meeùs, Nicolas. "Fundamental Line(s)." Conference paper, 2004. Available from the author's website:
link.
Drabkin, William, and Claudio Annibaldi. "'Bisogna leggere Schenker': Sull' analisi dell Preludio in Do Maggiore BWV 924 di Bach."
Rivista Italiana di Musicologia 24/1 (1989): 48-66.
Forte, Allen. "Prelude in C Major."
Allen Forte Electronic Archive. University of North Texas.
Link.
Forte, Allen, and Steven Gilbert.
Introduction to Schenkerian Analysis. New York: Norton, 1982.
Schenker, Heinrich.
Der Tonwille: Pamphlets in Witness of the Immutable Laws of Music: Offered to a New Generation of Youth. Translated by William Drabkin. Cambridge University Press, 2004.
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Note: I am embarrassed to say, thirty years later, that I seem to have mischaracterized Schenker's
Tonwille background by writing "the graph of the piece shows all six upper-voice tones as large notes (that is, as
Urlinie tones) with a subordinate
Anstieg leading to the ^5" (277). As you can see from both background and
Urlinietafel (foreground) above, this is not the case. Nevertheless, the basic characterization of the
Urlinie as consisting of all the labeled notes, except the opening ^3 & ^4, is correct, as it is consistent with Schenker's conception at the time. (He repeatedly refers to "the composing-out of the space of a fourth" in the
Tonwille essay.) If we do read the background strictly according to notation as in
Free Composition, then the background is an ^8-^7-^8 neighbor figure: see below (adapted from Drabkin and Annibaldi's example 6). This is Drabkin's reading above without the structural alto.