Burns actually apparently wrote two versions of this. Hea apparently had a gamekeeper friend named Davey with whom he liked to go walking. (Yes, I know all about the original Dainty Davey)
Anyway, I have a version of the "Rosy May " song called "Dainty Davey"
Here it is

Now rosy May comes in wi' flowers,
To deck her gay, green-spreading bowers;
And now comes in the happy hours,
To wander wi' my Davie.

Chorus.-Meet me on the warlock knowe,
Dainty Davie, Dainty Davie;
There I'll spend the day wi' you,
My ain dear Dainty Davie.

The crystal waters round us fa',
The merry birds are lovers a',
The scented breezes round us blaw,
A wandering wi' my Davie.
Meet me on, &c.

As purple morning starts the hare,
To steal upon her early fare,
Then thro' the dews I will repair,
To meet my faithfu' Davie.
Meet me on, &c.

When day, expiring in the west,
The curtain draws o' Nature's rest,
I flee to him that I loe' the best,
And that's my ain dear Davie.
Meet me on, &c.