The British-English adjective bone idle means utterly lazy or indolent.

Although other explanations are proposed in quotations 1 and 2 below, it seems that the noun bone in bone idle is used as an intensifier with adverbial force in the sense through to the bone, i.e., deeply and fundamentally.

This seems to be confirmed by the following from The vocabulary of East Anglia; an attempt to record the vulgar tongue of the twin sister counties, Norfolk and Suffolk, as it existed in the last twenty years of the eighteenth century, and still exists; with proof of its antiquity from etymology and authority (London: J. B. Nichols and Son, 1830), by the English philologist Robert Forby (1759-1825):

BONE-LAZY, BONE-SORE, BONE-TIRED, adj. so lazy, sore, or tired, that the laziness, the soreness, or the fatigue, seem to have penetrated the very bones. These compound epithets are certainly very expressive. The only objection to which they can be liable, seems to be, that they may be thought by some too poetical for common familiar language.

These are, in chronological order, the earliest occurrences of the adjective bone idle that I have found—in the first two texts, it is bane, the Scottish form of bone ¹, that occurs:

1-: From Supplement to the Etymological Dictionary of the Scottish Language (Edinburgh: Printed at the University Press; for W. & C. Tait […]; and Longman, Hurst, Rees, Orme, Brown, and Green, London – 1825), by the Scottish lexicographer John Jamieson (1759-1838):

BANE, s. Bone, S.]
[…]
Bane-dry, adj. Thoroughly dry, Clydes.; q. as dry as bones exposed to sun and wind. It seems to include the idea of the feeling of hardness that clothes have been thoroughly dried.
[…]
Bane-idle, adj. Totally unoccupied, Lanarks.
Can there be an allusion to one who has got nothing before him at a meal but a bone that he has already picked bare?

¹ Cf. origin of ‘bonfire’: a fire in which bones are burnt.

2-: From a letter that the Scottish historian and political philosopher Thomas Carlyle (1795-1881) wrote to his mother on 15^th May 1836—Thomas Carlyle implies that it is his mother who habitually uses the adjective “bane-idle”:
—as published in New Letters of Thomas Carlyle. Edited and annotated by Alexander Carlyle ². With Illustrations (London: John Lane The Bodley Head, 1904):

As to myself, for the last three weeks I have been going what you call bane-idle.*
* Bone-idle—i.e., as idle as an old bone.

² Alexander Carlyle (1843-1931) was Thomas Carlyle’s nephew.

3-: From Fair Rosamond; Or The Days of King Henry II. An Historical Romance (London: Henry Colburn, 1839), by the English poet and novelist Thomas Miller (1807-1874)—the following is from a dialogue between “Turstin, the son of Stur, the trusty blacksmith of Lincoln” and his wife:

“There are two guests in the smithy that we must give a meal’s meat, and a night’s shelter to, and—”
“Some lazy monks or other, I’ll warrant,” answered this rib of iron. “Marry! ³ thou mayest work;—all these bone-idle fellows find thee out.”

³ A variant of Mary (the name of the mother of Jesus), the obsolete exclamation marry expressed astonishment, outrage, etc.

4-: From the account of a court case, published in The Worcestershire Chronicle (Worcester, Worcestershire, England) of Wednesday 14^th September 1859:

The prisoner’s defence was that he was unable to work regularly in consequence of epilepsy, and could not maintain himself. The wife said he brought on his fits by drink, and that he was bone idle. When he was living with her she had great difficulty in getting him to go to his work in the morning.

5-: From the account of a court case, published in The Derby Mercury (Derby, Derbyshire, England) of Wednesday 17^th January 1872:

Frank Turner was summoned at the instance of Jane Turner, his wife, for having assaulted her on Monday. On that day defendant was lounging about the house and refused to go to work. His wife told him he was “bone idle,” whereupon the defendant knocked her twice and kicked her.

6-: From Familiar Talks with Young Christians, by the English Baptist minister and social reformer John Clifford (1836-1923), published in The General Baptist Magazine (London, England) of December 1872:

“Dear father, […] I know that if I had accepted the other (she would not call him by his name in such a relation) I should have had riches, station, comfort, and good connexions; but with them, one who has not been a kind son, who makes fun of his father, jeers his mother, never did a really kind and generous act so far as I know; is, as you say, “downright bone idle,” amiable enough, but very selfish, and has nothing that a girl could really love and revere! Would he make a good husband? How is it likely?”

7-: From the account of a court case, published in The North Cheshire Herald, and Hyde and Glossop News (Hyde, Cheshire, England) of Saturday 20^th September 1873:

A Runaway Apprentice.—A hatter’s apprentice, named James Broadhurst, was summoned to the Ashton County Sessions, on Wednesday, for being guilty of a misdemeanour and neglecting to fulfil his contract by unlawfully absenting himself from his work […]. James Haughton, the master’s son, denied having called the defendant an “idle skulk.” What he called him was simply “bone idle.”