This is the Scottish version of "Bye, Baby Bunting"...

Hushie ba, Burdie-beeton - Scottish Children's Songs - Scotland - Mama Lisa's World: Children's Songs and Rhymes from Around the World  - Intro Image

Notes

(1) Burdie-beeton is a fondling term for a little child as per the site, Dictionary of the Scots Language.
(2) Lammie/lambie is a term of endearment and a diminutive.
(3) On this site I found the following for "boulie" – "sweet-boulie – hard boiled sweet, gobstopper." Please email me if you have a better translation for "boulie" to put in the translation above.

Thanks and Acknowledgements

The illustration is from The Only True Mother Goose Melodies (published and copyrighted in Boston in 1833 by Munroe & Francis).