It was already surprising to find an entry for "bollix" in the American Heritage English Dictionary. But the root is traced to Old English "beallucas," noting an Indo-European root "bhel-" meaning "to swell." "Derivatives include boulevard, boulder, phallus, balloon, ballot, and fool." See for yourself.
My dad used to always say "That's all bollixed up" to mean, generally, screwed up, and I assumed that he was saying "bollocksed."
I think "bollocks" is a fair spelling of it, too, though it doesn't form the past tense very well (or, what sort of tense is that?).
"Bollocks" and "bollix" are pretty common over here in the yookay. Less so in the Americas, but we do know it over there, don't we?
Pro tip: "the dog's bollocks" is good, while "bollocks" is bad.