As Tolkien once put it: Go not to the elves for answers, for they will say both no and yes.

This seems like a fairly straightforward question, but the answer is anything but. The accuracy - and by accuracy we usually mean "utility" - of Bede as a source depends on the questions you're asking of him.

Speaking very generally, Bede is a useful source for many of the events he describes, as far as we can tell. There is a particular tendency early medieval historiography to privilege texts which describe events close to the date of the text's composition, and Bede is one of our few sources written relatively close to the events he describes. I am not comfortable with the linear way in which this is usually asserted, but it's a useful guiding principle; the closer something is written to when it happened, the closer the description will probably be to the events. But this is, as I said, general, and not true at many, many specific points.

And it's not like we have a superabundance of sources by which we might fact-check. As our archaeological record improves, we're getting a better sense of what our sources from this period are doing: how they construct a narrative, what they omit, what they emphasize. But the task is far from complete, and biased by where people are currently trying to build things.

So while Bede might give us a rough sense of what happened when, smart historians use his work on a more meta level. The Ecclesiastical History represents a world Bede wants to exist, and one which he believed existed. Reading the text this way, we learn some things about events, but we learn a lot more about Bede's world.