Well, as far as I know, this is the only piece written by Bukowski where he says that Barbara is his second wife. Yeah, it's poetry and you can't trust poets, but still... And the poem was published in 1959 and probably written in early 1959 or even late 1958, right after they divorced. It just makes perfect sense, literature and all.
I never trusted the FBI files anyway. Poets and the FBI fall into the same category as far as "truth" is concerned. If push comes to shove, I'd say that the poem is more reliable than those FBI files. But what do I know.