This song starts by moving back and forth between D minor and E minor. This is modal, but shifting back and forth between tonal centers: D dorian and E phrygian. At the end of the second line, though, it goes to D major instead of D minor. The D still feels like a tonal center, but with the next chord - a sort of D7 with an added 9th that's also heard in the intro - we soon find out that it's also modal (mixolydian).
The phrase modulation from D to B major that occurs in the bridge is easy enough, the F# in the melody being a common tone, but the move back from B major to the E minor to D minor progression is handled in a more difficult (and very beautiful) way. This occurs on the last note of the line "It's evident for anyone to see." On the two previous notes, we're on B, a common note between B major and E minor. The melody could have stayed on B on that last note of the line, when the chord changes to E minor, but instead it moves up to C, a non-chord tone.
To resolve the harmony, then, there is this really nice liaison between that last line of the bridge and the first line of the new (abbreviated) verse, "And I suppose they probably already do," where the melody doesn't land until the chord changes once again on the last note.