Three comments
This setting is basically the same as Gerry O’Connor’s recording on the Journeyman album. One of my students had asked for a setting of the tune that was easier to follow rhythmically, so this is my simplification.
More usually spelled as "Rossinure Hill", this is a great song from county Fermanagh especially as sung by the great Gaby McArdle. It was, and probably still is, very popular with northern musicians as an air. I play it myself. As such, it can be played quite freely, rather than "rhythmically". I truly hope I never hear it played as notated here.
Bessie the Beauty of Rossinure Hill
This song air is often associated with Fermanagh fiddler Mick Hoy. I came across his playing of it broadcast on RTE Radio 1 programme The Rolling Waves a few years ago, and recorded it on a mini disc. Now that the archive page of the programme is defunct, I have uploaded it onto SoundCloud: https://soundcloud.com/the-roving-bachelor/mick-hoy-bessie-the-beauty-of-rossinure-hill
And thanks to Mr. "Handed Down," we can watch Rev. Gary Hastings playing it on the flute: https://www.youtube.com/watch?v=VFvG49qaBSY
They both play the air in A dorian, not E dorian.
According to Hidden Fermanagh Book, Rossinure Hill lies between Derrygonnelly and Boho Mountain. The book also informs how Gabriel McArdle got the words of the song.