The Oxford English Dictionary gives under Beggars:

8. Special combinations. . . “beggar’s-bush, a bush under which a beggar finds shelter (name of ‘a tree near Huntingdon, formerly a noted rendezvous for beggars’ – Brewer), fig. beggary, ruin;”.

This is taken from E. Cobham Brewer’s Dictionary of Phrase and Fable (1868 and all editions until recently when the entry was dropped) which gave;

“Beggars Bush. To go by beggar’s bush, or Go home by beggar’s bush – i.e. to go to ruin. Beggar’s Bush is the name of a tree which once stood on the left hand of the London road from Huntingdon to Caxton; so called because it was a noted rendezvous for beggars. These punning phrases and proverbs are very common.”

This is partly true and partly false – perhaps more correctly this was false when it was first published, but through the influence of these two reference works has become common usage. It has been applied as a post facto explanation for the existence of the place name — see for example Donnybrook, Dublin and the histories of Dublin).

Origins

The literary usage meaning to go to ruin in correct, and such phrases were common. The statement that Beggars Bush sites were places where beggars met is unjustified, both here and generally. The history and source of the error here can be tracked. As Saunders records the Huntingdon site was recorded as King’s Bush in 1706 and by 1754 maps show King’s Bush only. (Philip Saunders Beggar’s Bush to King’s Bush, Records of Hunts, 1993, p.13 and Beggars Bush Revisited). Thus by the time Brewer first mentioned this site it had not been known by that name for more than a century.

Brewer derived his entry from other dictionaries, in which the derivation had become corrupted. This can be tracked back ultimately to Thomas Fuller’s story.  This appears in his popular History of the Worthies of England (1662, vol ii, p.98 in the 1840 edition).

“This is the way to Beggars-bush.”
“It is spoken of such who use dissolute and improvident courses, which tend to poverty; Beggars-bush being a tree notoriously known, on the left hand of London road from Huntingdon to Caxton. I have heard how King James, being in progress in these parts with Sir Francis Bacon the Lord Chancellor, and having heard that morning how Sir Francis had prodigiously rewarded a mean man for a small present; ” Sir Francis,” said he, “you will quickly come to Beggars-Bush; and I may even go along with you, if both be so bountiful.”

Anthologies

In addition to the Huntingdon books noted by Saunders several authors of collections of proverbs adopted Fuller’s phraseology, notably John Ray in A Compleat Collection of English Proverbs (1670) whose entry reads:

“This is the way to Beggars-bush. It is spoken of such who use dissolute and improvident courses, which tend to poverty. Beggars-bush being a tree notoriously known, on the left hand of the London road from Huntingdon to Caxton.”

Several others, including Grose and Hazlitt, include Fuller’s distinctive use of “dissolute and improvident” and “notoriously known”, together with the unnecessary detail that the tree was on the “left hand” of the road, when the natural description for most authors would have been to say it was on the right hand coming from London. None credit Fuller. Some compilers (Nare, and Farmer & Henly) are more original and note specific literary sources, and one mentions another site. Hazlitt used earlier proverb collections but records Ray as his source.

Neither Ray nor Fuller mention beggars in direct association with the site, so where did they come from ? That too can be tracked, this time working backwards from Brewer. His is the earliest work that directly associates beggars with this site. Brewer must also have had access to and used Halliwell’s Dictionary of Archaic and Provincial words (1847 and also 1850), whose entry reads “Beggar’s Bush; According to Miege a rendezvous for beggars. “To go by beggar’s bush,” to go on the road to ruin. Beggar’s Bush was also the name of a tree near London”. Brewer seems to have conflated the “rendezvous for beggars” with the Huntingdon site, which Halliwell appears to have moved even further than some of the cartographers.

Guy Miege

Halliwell’s states his source is Guy Miege, a Swiss writer based in London. I have been unable to trace this in the two most likely books, The Present State of Britain and Ireland (1723) and Miscellanea: Or, a Choice Collection of Wise and Ingenious Sayings (1694, re-issued in 1697 as Delight and Pastime; or, Pleasant Diversion for Both Sexes). Miege said he intended this collection to “serve to frame Minds to such Flashes of Wit as may be agreeable to civil and genteel Conversation”.

There is no evidence to suggest Miege had any local knowledge of the Huntingon site, or carried out any original research. Indeed, he is verifiably unreliable, describing Clause, a fictional character from Fletcher & Massinger’s play The Beggars Bush (1622) as the real King of the Beggars. Therefore, there is no reliable basis for a link between this site and actual beggars.

In contrast in an article in 1891 on Fenland Proverbs and Quaint Saying Charles Dack, a local historian, wrote: “He is on his way to Beggars bush,” in Huntingdonshire, applied to a spendthrift. The tree called “Beggar’s bush” is near Godmanchester.”

Entries from Anthologies

I have listed below the entries from anthologies I have traced which mention Beggars Bush.

The earliest collection of proverbs was Erasmus’s Collecteana Adagiorum, (1500) which was later expanded in numerous editions until it included more than 4,000 entries, but not Beggars Bush. It is not included in George Herbert’s Outlandish Proverbs (1640)

John Ray A Compleat Collection of English Proverbs London (1813 edition)
HUNTINGDONSHIRE
This is the way to Beggars-bush. It is spoken of such who use dissolute and improvident courses, which tend to poverty. Beggars-bush being a tree notoriously known, on the left hand of the London road from Huntingdon to Caxton.

Francis Grose A Provincial Glossary: with a collection of local proverbs, and popular superstitions, (2nd Ed) Hooper, London, 1790
HUNTINGDONSHIRE.
This is the way to Beggar’s-bush.
It is spoken of such who use dissolute and improvident courses, which tend to poverty; Beggar’s-bush being a well-known tree, on the left-hand of the London-road. from Huntingdon to Caxton. This punning adage is said to to be of royal origin, made and applied by King James I”, to Sir Francis Bacon, he having over generously rewarded a poor man for a trifling present.

Francis Grose’s, Dictionary of the Vulgar Tongue does not include Beggars Bush, which suggests it was by then regarded as a literary rather than vernacular phrase. However, it does include the following, which notably doesn’t include Beggars Bush as a haunt of beggars.
“A place of meeting. The rendezvous of the beggars were, about the year 1638, according to the Bellman, St, Quinton’s, the Three Crowns in the Vintry, St. Tybs, and at Knapsbury: there were four barns within a mile of London. In Middlesex were four other harbours, called Draw the Pudding out of the Fire, the Cross Keys in Craneford parish, St. Julian’s in Isleworth parish, and the house of Pettie in Northall parish. In Kent, the King’s Barn near Dartford, and Ketbrooke near Blackheath.”
The reference to the Bellman is to text from Thomas Dekker’s rogue literature pamphlet, The Guls Hornbook : and The Belman of London (1608). Much of the that work were taken from Thomas Harman’s Caveat for Common Cursitors (1566).

John Ray A Compleat Collection of English Proverbs (1670) (from 1813 edition)
HUNTINGDONSHIRE
This is the way to Beggars-bush. It is spoken of such who use dissolute and improvident courses, which tend to poverty. Beggars-bush being a tree notoriously known, on the left hand of the London road from Huntingdon to Caxton.

The 1768 edition of Ray is given as the source of a footnote on the place name by Alexander Dyce in his 1845 of the play in vol 9 of his ‘Works of Beaumont & Fletcher’.

R. Nare, A Glossary: or, Collection of words, phrases, names, and allusions to Customs, Proverbs etc, that have been thought to require Illustration, in the work of English authors particularly Shakespeare, and his contemporaries, London, Robert Triphook, 1822
BEGGARS BUSH, to go by. On of the numerous proverbial phrases that depended on a punning allusion to the name of a place. See Greene’s Quip, Harle. Misc. v.396. It means to go on the road to ruin.

James O. Halliwell, A Dictionary of Archaic and Provincial words, vol 1, (2nd ed), Boone, London, 1847.
Beggar’s Bush
According to Miege a rendezvous for beggars. “To go by beggar’s bush,” to go on the road to ruin. Beggar’s Bush was also the name of a tree near London . . . A similar phrase “We are brought to beggar staff” occurs in the Plumpton Correspondence, p.199.
[Also refers to usages by John Cleveland and Henry Porter]
[The entry is the same in the Third Edition 1850]

E. Cobham Brewer, Dictionary of Phrase and Fable, Cassell, London, 1868
Beggar’s Bush
To go by beggar’s bush, or Go home by beggar’s bush — i.e. to go to ruin. Beggar’s bush is the name of a tree which once stood on the left hand of the London road from Huntingdon to Caxton; so called because it was a noted rendezvous for beggars. These punning phrases and proverbs are very common.

W. C. Hazlitt, English proverbs and proverbial phrases collected from the most authentic sources, alphabetically arranged and annotated, with much matter not previously published, 1869, p. 401
This is the way to Beggar’s bush Huntingdonshire.
It is spoken of such who use dissolute and improvident courses, which tend to poverty. This particular Beggars’-bush being a tree notoriously known, on the left-hand of the London road, from Huntingdon to Caxton – R”
[R for Ray indicating that this is the earliest source he found]
Hazlitt is also responsible in the same work for a Beggars Bush at Gorton, Manchester, which is likely to be a mistranscription.

J. S. Farmer and W. E. Henly, A dictionary, historical and comparative of the heterodox speech of all classes of society for more than three hundred years. With synonyms in English, French, German, Italian, etc Privately Published, London (1890)
BEGGARS BUSH TO GO BY BEGGARS BUSH, phr (old) means to go to ruin. Otherwise explained as follows: [extracts from 12 Ingenious Characters and Brewers]. Russell Hill, near Croydon, where the Warehousemen’s and Clerk’s schools are, is known locally as BEGGARS BUSH.

An honourable exception to these is Eric Partridge. The entry against Beggars Bush in his Dictionary of Slang and Unconventional English (1937 and numerous since, though I have not checked a first edition) gives :

beggar’s bush, go (home) by

To be ruined: late C.16–19; in 1564, Bullein has a rare variant, thus: ‘In the ende thei go home …by weepyng cross, by beggers barne, and by knave’s acre,’ Apperson. Beggars have always, in summer, slept under trees and bushes; in winter, if possible, they naturally seek a barn.

There is no entry for the phrase in Bartlett Jere Whiting’s Early American Proverbs and Proverbial Phrases (1977)