Without hearing the song this is what is likely happening:
F# I stumbled out of bed
D#m I got ready for the struggle
F# I smoked a cigarette
D#m - C# And I tightened up my gut
This is fairly straight-forward, moving along in the key of F#: I-vi-I-vi-V
From there, it is a deceptively cadences to "B" (IV) instead of the expected return to "F#":
B - Bm - G#m I said this can't be me
A# - E - D#m
Must be my double
F# - B And I can't forget... (etc)
In this passage, he is using "B" as a local tonicization by treating as a pivot chord and implying a move to B major. Using the first be as a pivot, we'd analyze the chords in the key of B major: I-i-vi-VII-IV-iii-V-I.
Obviously, with a VII, something odd is happening. It can't be a borrowed chord from the subdominant (if we were thinking of the entire passage in F#) because as a leading tone chord, it would be fully-diminished. So how does the A# chord function?
My answer is that the chord in of itself is inherently non-functional in terms of harmonic progression, but is function in creating some very nuanced inner-lines. In order to understand what's really happening here we need to look at the text along with the chords.
In order to understand the second part, we must first look at the top stanza highlighted above. Notice how an association is developed between the personal pronoun "I" and the chordal motion from I-vi. Each line begins with "I" and the chord is either I or vi.
Now, looking at the second stanza, notice how the first line also contains the personal pronoun "I" along with a motion of I-vi (now in B major). This is where things get interesting. The straight-forward harmonic motion of the first stanza mirrors the confident, concrete observations and descriptions of actions detailed in the text. It is only when the character begins questioning themselves that the harmonic motion begins to get wonky, which brings us back to the second stanza...
Notice how the chord quality changes from B to Bm with the phrase "I said this can't be me" - already the author is blurring the lines of functional tonality here in the same way the character in the song is confused. This fact is further supported by chromatic noodling of the inner-lines which I will outline below. First, let us take a pitch inventory of the chords used:
- B = B, D#, F#
- Bm = B, D, F#
- G#m = G#, B, D#
- A# = A#, C##, E#
- E = E, G#, B
- D#m = D#, F#, A#
- F# = F#, A#, C#
Now I will arrange them to have smooth voice-leading to better illustrate the chromatic noodling in the inner lines:
- B = B, D#, F#
- Bm = B, D, F#
- G#m = B, D#, G#
- A# = A#, C##(D), E#(F)
- E = B, G#, E
- D#m = A#, F#, D#
- F# = A#, F#, C#
I have italicized all of the notes that move chromatically by step from the previous chord. As you can see by the numerous chromatic half-step motion between chords, Cohen is using the tried and true technique of word painting to emphasize the text's meaning. In this case, the text suggests a blurring of identity through duality. Thus, Cohen uses chromatic half-step motion and local tonicization to the subdominant in F# major to suggest tonal implications of duality.
In the last line of the second stanza, we see a V-I in B major (an Authentic Cadence) that supports the text "And I can't forget...". Such harmonic reinforcement (an Authentic Cadence is a strong cadence) suggests a "snapping" back to reality as the narrator of the song realizes that he cannot forget. This harmonic motion provides stability to the wandering harmony of the previous lines, as if resuming where it had left off when beginning the section. From here, Cohen could easily use the "B" as a pivot chord to move back into F# major and continue on. (I don't know what happens as I have not heard the piece.)