The reference is to Bede's Ecclesiastical History, Bk. I, ch. 3. The relevant passage reads:

In the year of Rome 798 [an error for 796, which would be AD 43] the Emperor Claudius, fourth after Augustus, wishing to prove that he was a benefactor to the State, sought to make war everywhere and to gain victories on every hand. So he made an expedition to Britain, which had apparently been roused to rebellion because of the refusal of the Romans to give up some deserters. He crossed to the island which no one either before or after Julius Caesar had dared to invade until then, and without any fighting or bloodshed he received the surrender of the greater part of the island within a very few days. He even annexed to the Roman empire the Orkneys, some islands which lie in the Ocean beyond Britain. [Orcadas etiam insulas ultr Brittaniam in Oceano positas Romano adicit imperio.] He returned to Rome only six months after.

This entire passage, with only minor changes, is lifted almost verbatim from Orosius, History Against the Pagans, Bk. VII (or see the Latin), ch. 6. Bede then continues his chapter with passages taken from Eutropius, Abridgement of Roman History, Bk. 7, ch. 13 and ch. 19. This blatant plagiarism of sources is fairly typical for all of Bede's Book I, which describes the history of Britain before the mission of Augustine in 597.

Bede was writing in northern England around 734. Orosius' History Against the Pagans had been written by a churchman living in eastern Spain in the early 400s. He intended his History to complement Augustine of Hippo's City of God by showing how Christianity improved the world. One of his consistent tropes is that Roman emperors who anticipated Christian virtues were successful, whereas Roman emperors who would be condemned according to Christian values had been unsuccessful. Claudius was clearly meant to be a positive example, followed by the negative example of Nero. As such, Orosius should not be trusted as being completely accurate.

Bede, however, was only interested in the passages most relevant to Britain, which obscures Orosius' intended meaning that the rise and fall of virtue corresponds to the rise and fall of empires. This is one of the dangers of reading Bede's Ecclesiastical History too literally, particularly in the early chapters. He creates a great encyclopedia of sources on early Britain, but he does violence to the original contexts of the passages that he borrows. It should be remembered that Bede had different interests and motivations from the sources he used, and that none of these writers was trying to write the 'objective history' (if such a thing could exist) that modern scholars would love to have.

That's not to deny that the Ecclesiastical History has great value as a source. It certainly does: it gives us a particularly good window into the concerns of an eighth-century churchman, and Bede seems to draw on real knowledge (and archives!) as he discusses the church in England after the missionary Augustine arrived in 597. If you're interested in learning more about what Bede was up to as he wrote, Walter Goffart's Narrators of Barbarian History (1988) is indispensable, or you can read his shorter article summary "The Historia Ecclesiastica: Bede's Agenda and Ours," Haskins Society Journal 2 (1990): 29-45.

And a quick note about the Orkneys before proceeding on to the Faroes. These islands would become a major hub during the Viking Age, and most travelers moving between the North and Irish Seas would have spent at least a night there before moving on, but this traffic would still have been rather small in Bede's day, so he probably wasn't inherently fascinated with the Orkneys. (The only other mentions of the Orkneys that I found were in Book I, ch. 1, which is just a brief reference and is again borrowed from Orosius, and Book V, ch. 24, which is a chronological summary and merely references the earlier text.) I think it's safe to assume that they appear in this account because Orosius wanted to emphasize how great Claudius was, reaching the far edges of the known world, and Bede simply took this for what it's worth without ever questioning its accuracy.

---

Regarding the islands further north, I misread the map and assumed you meant the Faroes instead. Some discussion on that follows, and my response to your actual question about the Shetlands follows later down the thread. Bede makes no reference to the Faroe Islands and might not have known about them. The Faroes may have been inhabited at some point around 300-500 AD, but there's no reason to assume that information of the Faroes would have reached Bede, or if it did, that a person like Bede would think it important. Bede drew most of his Book 1 from written sources, so adding something new from oral history might not have interested him, even if he had access to the information.

Our information on the later settlement of the Faroe Islands is patchy, and much of it resembles what we know about Iceland: hints of Irish activity, followed by large-scale Norse migration in the late 800s. The problem is that some of the medieval writers who recorded this information might have been confused, or perhaps they were filling in blanks by borrowing from complementary traditions about different places. And unfortunately, whereas archaeological sites in Iceland can be finely dated by determining whether artifacts fall above or below certain layers of volcanic ash, the Faroes offer no such diagnostic opportunities. The article linked above indicates that at least one site has produced a carbon date around the time of Bede, so the Faroes may have been occupied at that time. Unfortunately, later settlement has largely obliterated any traces of settlement before the 800s, so it's very hard to interpret what this isolated find might mean.

Edit: Map error on my part. The Faroes are somewhat irrelevantly discussed here, although I've tried to answer OP's original question about the Shetlands further down the thread.