This is a traditional round, likely dating back to Medieval times. This can be found in any variety of permutations, nearly always starting with the first verse, which is repeated at the end. I don't know that any version of the song has been recorded on it's own, but I do know that Peter, Paul and Mary sang the third verse as part of a traditional folk medly.

Rose, rose, rose red
Will I never see the wed
I will marry at thy will, sire
At thy will

Ding, dong, ding, dong
Wedding bells will not be rung

Not at thy will.

I won't be my father's Jack
I won't be my mother's Jill
I will be a fiddler's wife
And fiddle as I will

I won't be my mother's toy
I won't be my father's tool
I will be a terrier's wife
And tarry where I will

Hey, ho, nobody home
Meat or drink or money have I none
Still, I will be very merry
Hey ho hum

Ding dong, ding dong
Churchbells ring on a Sunday morn
Carve your name on a moss covered stone
A moss covered stone

Oh poor bird
Why art thou
Flying through the shadows
Of this dark hour

Ah, my Love
Thou Lovest me
Then quickly come to save her
who dies for thee

Oh poor bird
High in flight
High above the mountain tops
On this cold night

Commonly, the first line is also "Rose, rose, rose, rose" as well as the second line of the sixth verse being "Wedding bells on an April morn."