The text Masato quotes is in the DT, here: COME TO THE BOWER, with tune, uncredited to Moore.

A music sheet of the other lyric can be seen at The Lester Levy Sheet Music Collection:

Will You Come to the Bower No date of publication or composer[s] named.

There are quite a few examples of the "shaded for you" lyric from the first half of the 19th century at Bodleian Library Broadside Ballads, all credited to Moore in the catalogue, though not on most of the sheets themselves. There are also a couple of other texts which prescribe the tune, one of which is dated between 1744 and 1768, before Moore was born, so we may safely assume that he based his text -or texts- on an earlier song. Here is a set of lyrics taken from one, Will you come to the bower ("Will you come to the bower I have shaded for you ...") Printed & Sold by Th. Ash, 9, Red Lion Court, Watling St. (no date), "Sung by Mr. [Charles Benjamin] Incledon":


WILL YOU COME TO THE BOWER
(Words by Thomas Moore)

1. Will you come to the bow'r I have shaded for you
Our bed shall be roses all spangled with dew
Will you, will you, will you, will you come to the bow'r
Will you, will you, will you, will you come to the bow'r.

2. Then under the bower on roses you'll lie
With a blush on your cheeks and a smile in your eye.

3. But the roses we press shall not rival your lip
Nor the dew be so sweet as the kisses we'll sip.

4. And oh! for those joys that are sweeter than dew
From languishing roses or kisses from you.

Two different texts, and evidently an earlier one, too. Colm O Lochlainn (Irish Street Ballads), printed a set of the "travelogue" text, with music, from P. Walsh of Clogher Valley, Tír Éoghain; no author is mentioned. I'd have thought that O Lochlainn would have known if Moore was responsible for it, but maybe not. At any rate, it seems likely that the short text is the older of the two we have here.