what does the phrase "Lay the bent to the bonny broom" means?
You'll never get an answer to this one! Haha ) It's folklore, <em>riddle</em> and dialect mixed together. Broom here is almost certainly the plant https://ru.wikipedia.org/wiki/%D0%94%D1%80%D0%BE%D0%BA%D0%BE%D0%B2%D1%8B%D0%B5
which the English word for 'веник' come from originally. The 'bent' might not be from 'to bend,глагол' but another obscure plant instead. Basically, it's totally obscure. It could very well be 'инсинуация,' something about beds, or something to do with herbal folklore...
In the first link, it's sung in Scottish dialect. Southern or Eastern I'd say. I'm not sure if it's strongly regional - I grew up on the English side of the borders area, but can't tell the regions apart well. I can tell Glasgow and the highlands apart from the rest, but not the south and east from eachother. The second is a straightforward american version.