The notion that the Boles Barrow Bluestone came from Boles Barrow is based on an undated footnote William Cunnington added to his copy of a letter he had sent to H P Wyndham in 1801. In which he had described the large stones in the barrow he found when excavating it that year as "are of the same species of stone as the very large Stones at Stonehenge". In other words he was saying they were sarsens. Further on in the letter he notes he has brought ten such stones to his house, not explicitly saying they were or were not from the barrow. His later footnote to himself is ":Since writing the above I discover amongst them (presumably the stones in his garden) the Blue Hard Stone also, ye same to some of the upright stones in ye inner circle at Stonehenge". (Mike Pitts Hengeworld 2000 p 199-200)
So the linking of any bluestone to the barrow is not clear, even without the disparity between the weights of the Boles Barrow bluestone (611kg) and the weights of stones Cunnington records (13-90kg)
So at some time looking at his rockery he realises he has inadvertently got a bluestone in there, and as some of the rockery may, and only may, have come from Boles Barrow it is assumed that is where it came from. Even though he didn't notice it at the time.
In Colt Hoare's description of the excavation of Boles Barrow - see the bottom of this post - there is no note of the discovery of a bluestone.at all.
But he did record finding "a large piece" of one of the Stonehenge Bluestones in a tumulus in the Stonehenge triangle, Amesbury G4, for details search for it on Simon Banton's Barrow Map and here it is recorded in Colt Hoare's book:
Click to enlarge
https://historicengland.org.uk/listing/the-list/list-entry/1012387
Sir Richard Colt Hoare The History of Ancient Wiltshire 1812 Volume 1. Boles Barrow Excavation
In this ride I shall ascend the hills at the back of Sir William A'Court's demesne, and proceed over Nanny Down towards Bowls Barrow. At the upper end of Heytesbury field and near the summit of the hill, is a flat barrow ploughed over, which Mr. Cunnington opened in 1800, and found about a foot under the surface, a layer of flints that extended nearly over the whole tumulus, intermixed with fragments of thick and coarse pottery; and was much surprized in finding ten small brass Roman coins of the Emperors Constantine, Valentine I. and II. and Arcadius, together with some pieces of the fine red Samian pottery. From the discovery of these articles, viz. first, the rude pottery, and afterwards the fine Samian ware, and coins, we may conceive this to have been occupied both by the Celtic and Romanized Britons.
On the summit of the hill we meet the great track-way, and crossing it come to a large tumulus named BOWLS BARROW; its length is one hundred and fifty feet at the base; its width ninety-four feet, and its elevation ten feet and a half, though it appears to the eye much higher; the broad end points towards the east. This large barrow was opened by Mr. Cunnington in 1801, and attended with much labour. He began by making a section of considerable width and length across the barrow near the east end, and at the depth of two feet nine inches found a human skeleton lying south-west and north-east, and with it a brass buckle, and two thin pieces of the same metal. Towards the centre of the barrow, were two other skeletons interred, with their heads towards the south, and one of them lying on its side. The interior parts of the barrow were composed entirely of white marl stone to the depth of four feet and a half: this was succeeded by a ridge of large stones and flints, which extended wider as the men worked downwards. At the depth of ten feet and a half, which was the base of the barrow, was a floor of flints regularly laid, and on it the remains of several human bodies deposited in no regular order. It appeared therefore, that they had been thrown together promiscuously, and a great pile of stones raised length-ways along the centre of the barrow over them. This pile (in form like the ridge of a house), was afterwards covered with marl excavated from the north and south sides of the barrow, the two ends being level with the plain. Although four men were employed for three days, they could not explore more than the space of about six feet by ten; yet in this small portion they found fourteen skulls, one of which appeared to have been cut in two by a sword. It is rather singular, that no fragments whatever of pottery, charred wood, or animal bones, were found in the course of the above operations.
At a subsequent period Mr. Cunnington made a second attempt on this tumulus, by opening more ground both at the east as well as west end; at the former he found the heads and horns of seven or more oxen; also a large cist close to the skeletons; but owing to the great height of the barrow, and the large stones continually rolling down upon the labourers, he was obliged to stop his operations.