Here's a wild guess as to the meaning of the phrase, 'Lay the Bent to the Bonny Broom' (as least as wild as some of the folkloric explanations quoted above!). Perhaps its got something to do with lighting, or shedding light(?)

A 'bent' is a Rush (a plant in the genus Juncus). In the days before gas and electricity, poor cottage dwellers, who couldn't afford candles, would light their cottages with 'rush lights'. The Soft Rush (J. effusus) consists of a clump of cylindrical stems, between 1 and 2 feet high, with a tuft of brownish flowers sprouting from the side of each stem quite near the top. The stem is covered with a smooth green skin or rind. If this skin is peeled away it reveals a continuous white pith. The cottager dwellers would peel each rush stem to expose the pith, which would then be soaked in tallow or lard. This oily taper would be held in a clip and burned to produce a (probably very feeble!) light. Perhaps the clip would be made from the flexible stems of the shrub called Broom (Cytisus scoparius)?

Presently, I can't think of any way to check this theory ...