This one brings back memories. I recall using it in a presentation of love songs, titled 'The Boy Who Pu'd the Rose', a couple of decades ago at a festival in Toodyay, Western Australia. Nice song - I had forgotten it completely. My transcription follows. I am not certain about the phrase is square brackets in stanza 4, but that is what it sounds like - someone else may be able to confirm or correct:

THE BONNY BLUE HANDKERCHIEF

Oh, as I was out a-walking one evening in May
I spied a fair maiden, she trippin' so gay
I spied a fair maiden, sweetly she did sing
And she tossed her blue handkerchief under her chin

'Oh, where now are you going to my own pretty maid
Where are you going to so kindly I said'
'I'm going down to yon cottage in order to spin'
And she tossed her blue handkerchief under her chin

'Now, why do you wear it, miss, all to one side'
'It is the fashion of my country', the lady replied
'And the fashion of my country I like to be in'
And she tossed her blue handkerchief under her chin

Well, I coaxed and I flattered her on for a while
I coaxed and I flattered her till she did smile
She said, 'I have no time for flattery [of an inn]
And she tossed her blue handkerchief under her chin

Oh, to kiss her sweet lips I did try to begin
She said, 'Now stop, young man, I'll tell you one thing
He who kisses my sweet lips must produce a gold ring'
And she tossed her blue handkerchief under her chin

I put me hand into me pocket, pulled out the gold ring
'Take this, dear lady, I'm one of those men
And I will be as true as the colour going in
To the bonny blue handkerchief under your chin

Well, this couple they got married, I'm happy to say
This couple they got married in autumn so gay
And now the fair spinner she wears a gold ring
And he wears the blue handkerchief under his chin

Source: transcription from Aengus 'Aengus' Tara LP 2001 [1978].

--Stewie.