I looked in four rounds books, and the only one that had "Rose, Rose" was Sol Weber's Rounds Galore. The version that's in the Digital Tradition is also in the Rise Up Singing songbook, which has a very nice Rounds section:

Rose, Rose, Rose, Rose
Shall I ever see thee wed
Aye, marry, that thou wilt
If thou but stay.^^^

It's a terribly common round, and that may be why the songbooks don't include it. Besides, I think the second pair of lines is problematic - they're neither interesting nor memorable, and nobody really knows what's right. Now, a think a far more classic round is "Row, Row, Row Your Boat" - everybody remembers that one.

-Joe-