Beggars Bush is noted in many anthologies (e.g. Brewer's Dictionary of Phrase and Fable) as a haunt of beggars and this is frequently given as an explanation for the origin of the name. I have analysed 120 sites where the name is record and can say with confidence that it is not. Brewer's entry is created from an concatenatiuon of earlier anthologists and can be traced back to Thomas Fuller in 1662 who said the phrase was used to mean "to go to ruin". The "bush" is symbolic as in precursor phrases, e.g. (1506)"we are brought to begger staffe"and (1564) 'go home many miles, by foolam crosse, by weepyng cross, by beggers Barne, and by knaues Acre". The type example is in the pamphlet Her Protection for Women (London, 1589) by the pseudonymous Jane Anger;
"The great Patrimonies that wealthy men leave their children after their death, make them rich: but vice and other marthriftes happening into their companies, never leave them until they bee at the beggers bush, where I can assure you they become poore."
I am a great fan of John Taylor, The Water Poet, who mentions two Beggars Bushes in the dedication to his Praise, Antiquity and Commodity of Beggary, Beggars & begging, etc. (1621). Taylor would have passed the Beggars Bush site near Godminster during his Pennyles Pilgrimage (1618) but makes no mention of the site in that work. He was almost certainly aware of the place name from a map, as it is a prominent symbol on Saxton's map (1576) and copied subsequently by almost every other mapmaker. The wonderful woodcut showing two ragged beggars under Beggars Bush, but it bears no relationship to the text, which is Taylor's usual doggerel and does not mention itself Beggars Bush. I suspect that it was either reused or designed for another pamphlet now lost or never published.