[Halfir]

I suspect the Bounders of The Shire had a two-fold function. The first one is that described in the Prologue to FOTR , which is effectively a 'policing function' to make sure that the 'wrong sort' don't get into the Shire.

The second function is implicit in their name. It was a tradition in medieval England, that every May Day (I am not absolutely certain of the date but it was certainly in May) the 'bounds' or perimeters of landholding were 'beaten'- to establish and confirm boundary distinctions - land in those days being granted by charter from the Crown or feudal overlord. As land was such a precious commodity, exact boundaries were important to landowners and villages.

An interesting aspect of the ceremony was that at every important point along the boundary the local boys were beaten or thrown into the village pond, so that in later life, if boundary disputes arose, they would have a very clear memory of what the boundaries were!

While Tolkien does not explicitly refer to this practice and aspect of bounding, I suspect that given his extensive philological knowledge, he had this image also in mind when he wrote.