The tune for "Ah, Poor Bird" is not the same as for "Rose, Rose..." and that's why it doesn't seem to scan; it harmonizes well when they're sung simultaneously.

Here it is in abc notation. (More info on that here, but in short, the letters are the notes you'd expect. Capital letters for the octave from middle C, small letters above middle C. In this case, it's based on an 1/8th note, so "D2" is a quarter note D, "F4" is a half note F, "dd" is two eighth note high d's, etc.)

X:1
T:Ah Poor Bird
C:trad.
N:round (compatible with Joan, Joan/Rose, Rose)
Q:1/4=110
V:1
M:4/4
L:1/8
K:Dm
D2 E2 F4 |F2 G2 A4 |GA dd cd AA |G F2 E2 D3 |]

~ Becky in Tucson